diff --git a/frontend/src/lib/components/common/table/EditInForkButton.svelte b/frontend/src/lib/components/common/table/EditInForkButton.svelte
index fe5c6bc193..ad0ef372a7 100644
--- a/frontend/src/lib/components/common/table/EditInForkButton.svelte
+++ b/frontend/src/lib/components/common/table/EditInForkButton.svelte
@@ -31,11 +31,15 @@
 <!-- title on the wrapper, not on <Button>: Button renders its `title` prop only in the
      <button> branch, so the <a> branch taken here (href is set) would silently drop it.
      On the wrapper it also covers the icon and padding, not just the label text. -->
-<div title={label}>
+<!-- Like the row's Edit button: shown on hover, focus or keyboard selection. -->
+<div
+	title={label}
+	class="invisible group-hover/row:visible group-focus-within/row:visible group-data-[row-keyboard-selected=true]/row:visible"
+>
 	<Button
-		variant="subtle"
-		wrapperClasses="max-w-56"
-		unifiedSize="md"
+		variant="accent"
+		wrapperClasses="max-w-40"
+		unifiedSize="sm"
 		startIcon={{ icon: Pen }}
 		{href}
 		onClick={(e) => onEditInForkClick(e, itemType, path, { hasHref: true })}
diff --git a/frontend/src/lib/components/common/table/Row.svelte b/frontend/src/lib/components/common/table/Row.svelte
index 49022bfa45..2c2d5ffd08 100644
--- a/frontend/src/lib/components/common/table/Row.svelte
+++ b/frontend/src/lib/components/common/table/Row.svelte
@@ -17,6 +17,7 @@
 		EMPTY_CELL_DASH,
 		HOME_TABLE_BADGE_GRID,
 		HOME_TABLE_GRID,
+		HOME_TABLE_ROW_SEPARATOR,
 		isHomeTable
 	} from '$lib/components/home/homeTable'
 
@@ -78,7 +79,8 @@
 		badges?: import('svelte').Snippet
 		/** Badge groups the home table gives a column each; elsewhere they render
 		 * inline, in this order, after `badges`. */
-		languageBadge?: import('svelte').Snippet
+		/** Appended to the path line, e.g. a script's language. */
+		pathSuffix?: string | undefined
 		tagBadges?: import('svelte').Snippet
 		draftBadge?: import('svelte').Snippet
 		sharedBadge?: import('svelte').Snippet
@@ -122,7 +124,7 @@
 		workspaceId,
 		depth = 0,
 		badges,
-		languageBadge,
+		pathSuffix = undefined,
 		tagBadges,
 		draftBadge,
 		sharedBadge,
@@ -206,7 +208,8 @@
 		data-row-keyboard-selected={keyboardSelected ? 'true' : undefined}
 		class={twMerge(
 			HOME_TABLE_GRID,
-			'group/row relative w-full pl-5 pr-3 py-2.5 rounded-md',
+			'group/row relative w-full pl-5 pr-3 py-2.5',
+			HOME_TABLE_ROW_SEPARATOR,
 			disabled ? 'opacity-25' : 'hover:bg-surface-hover',
 			inSelectionMode ? 'cursor-pointer select-none' : '',
 			rowSelection?.selected
@@ -224,8 +227,12 @@
 				class="absolute inset-0"
 			></a>
 		{/if}
-		<!-- The kind icon, swapped for the checkbox on hover and in selection mode. -->
-		<div class="relative z-[1] w-4 h-4">
+		<!-- The kind icon, swapped for the checkbox on hover and in selection mode. In the
+		     tree it moves right by the same depth offset as the name, under its folder. -->
+		<div
+			class="relative z-[1] w-4 h-4"
+			style={depth > 0 ? `transform: translateX(${depth * 16}px);` : ''}
+		>
 			<div
 				class={twMerge(
 					'absolute inset-0',
@@ -425,8 +432,14 @@
 					'text-emphasis flex-wrap text-left text-xs min-w-0',
 					homeTable ? 'font-normal' : 'font-semibold',
 					titleBadge ? 'inline-flex items-center gap-2' : '',
+					homeTable && !titleBadge ? 'line-clamp-2 break-words' : '',
 					linked ? 'group-hover/row:underline decoration-gray-400' : ''
 				)}
+				title={homeTable && !customSummary
+					? !summary || summary.length == 0
+						? displayPath
+						: summary
+					: undefined}
 			>
 				{#if customSummary}
 					{@render customSummary?.()}
@@ -437,11 +450,6 @@
 				{/if}
 				{@render titleBadge?.()}
 			</div>
-			{#if !inlineBadges && languageBadge}
-				<div class="flex items-center shrink-0">
-					{@render languageBadge()}
-				</div>
-			{/if}
 			{#if !inlineBadges && tagBadges}
 				<div class="relative z-[1] flex items-center gap-1 shrink-0">{@render tagBadges()}</div>
 			{/if}
@@ -452,10 +460,9 @@
 			{#if homeTable}
 				{@render inlineFavorite()}
 			{/if}
-			{#if inlineBadges && (badges || languageBadge || tagBadges || draftBadge || sharedBadge || labelBadges)}
+			{#if inlineBadges && (badges || tagBadges || draftBadge || sharedBadge || labelBadges)}
 				<div class="relative z-[1] hidden lg:flex flex-row gap-1 items-center shrink-0">
 					{@render badges?.()}
-					{@render languageBadge?.()}
 					{@render tagBadges?.()}
 					{@render draftBadge?.()}
 					{@render sharedBadge?.()}
@@ -469,6 +476,9 @@
 			{:else}
 				{path}
 			{/if}
+			{#if pathSuffix}
+				<span class="opacity-75">· {pathSuffix}</span>
+			{/if}
 		</div>
 	</div>
 {/snippet}
diff --git a/frontend/src/lib/components/common/table/ScriptRow.svelte b/frontend/src/lib/components/common/table/ScriptRow.svelte
index 5c65d64acf..b72ddb1a9b 100644
--- a/frontend/src/lib/components/common/table/ScriptRow.svelte
+++ b/frontend/src/lib/components/common/table/ScriptRow.svelte
@@ -29,7 +29,6 @@
 	import { isDeployable } from '$lib/utils_deployable'
 
 	import type DeployWorkspaceDrawer from '$lib/components/DeployWorkspaceDrawer.svelte'
-	import { LanguageIcon } from '../languageIcons'
 	import {
 		Archive,
 		Calendar,
@@ -52,7 +51,7 @@
 	import { Drawer, DrawerContent } from '..'
 	import NoMainFuncBadge from '$lib/components/NoMainFuncBadge.svelte'
 	import RowLabels from './RowLabels.svelte'
-	import { isHomeTable } from '$lib/components/home/homeTable'
+	import { defaultScriptLanguages } from '$lib/scripts'
 	import Popover from '$lib/components/Popover.svelte'
 	import Tooltip from '$lib/components/Tooltip.svelte'
 	import { getDeployUiSettings } from '$lib/components/home/deploy_ui'
@@ -104,7 +103,6 @@
 	}: Props = $props()
 
 	const dispatch = createEventDispatcher()
-	const iconSize = isHomeTable() ? 12 : 14
 
 	async function archiveScript(path: string): Promise<void> {
 		await ScriptService.archiveScriptByPath({ workspace: $workspaceStore!, path })
@@ -172,14 +170,12 @@
 	workspaceId={$workspaceStore ?? ''}
 	canFavorite={!script.draft_only}
 	editedAt={script.created_at}
+	pathSuffix={script.language
+		? (defaultScriptLanguages[script.language] ?? script.language)
+		: undefined}
 	{depth}
 	{rowSelection}
 >
-	{#snippet languageBadge()}
-		{#if script.language}
-			<LanguageIcon lang={script.language} width={iconSize} height={iconSize} />
-		{/if}
-	{/snippet}
 	{#snippet tagBadges()}
 		{#if script.lock_error_logs}
 			<Badge color="red" baseClass="border border-red-200">Deployment failed</Badge>
diff --git a/frontend/src/lib/components/home/ItemsList.svelte b/frontend/src/lib/components/home/ItemsList.svelte
index 3e73c4cfb1..82a2623c58 100644
--- a/frontend/src/lib/components/home/ItemsList.svelte
+++ b/frontend/src/lib/components/home/ItemsList.svelte
@@ -18,7 +18,9 @@
 	} from '$lib/gen'
 	import { resource } from 'runed'
 	import { getDraftItems } from '$lib/workspaceDrafts.svelte'
-	import { disableHubStore, userStore, workspaceStore } from '$lib/stores'
+	import { disableHubStore, userStore, userWorkspaces, workspaceStore } from '$lib/stores'
+	import { editInForkAllowed } from '$lib/utils/editInFork'
+	import { isCloudHosted } from '$lib/cloud'
 	import { useOperatorBuilderFlows } from '$lib/operatorWriteRights'
 	import type uFuzzy from '@leeoniya/ufuzzy'
 	import {
@@ -67,7 +69,13 @@
 	import BulkActionsBar from './BulkActionsBar.svelte'
 	import { HomeSelection, setHomeSelection, toBulkItem } from './homeSelection.svelte'
 	import { HomeActivity, setHomeActivity } from './homeActivity.svelte'
-	import { HOME_TABLE_BADGE_GRID, HOME_TABLE_GRID, setHomeTable } from './homeTable'
+	import {
+		HOME_TABLE_BADGE_GRID,
+		HOME_TABLE_GRID,
+		HOME_TABLE_ROW_SEPARATOR,
+		HOME_TABLE_WIDE_ACTIONS,
+		setHomeTable
+	} from './homeTable'
 	import Checkbox from '../common/checkbox/Checkbox.svelte'
 
 	const operatorBuilderFlows = useOperatorBuilderFlows()
@@ -1495,6 +1503,16 @@
 				)
 			: items
 	)
+	// A row the user cannot edit offers "Edit in fork", which needs a wider actions column.
+	let tableStyle = $derived(
+		!isCloudHosted() &&
+			editInForkAllowed($workspaceStore, $userWorkspaces) &&
+			((treeView ? treeSource : items) ?? []).some(
+				(it) => !showEditButtons || !('canWrite' in it) || !it.canWrite
+			)
+			? HOME_TABLE_WIDE_ACTIONS
+			: undefined
+	)
 	// Remount identity: only a *mode* change (workspace, selected owner, entering/leaving
 	// search, label filter) restructures the tree, so only those key the {#key} remount.
 	// A sort/archive/library/kind change keeps the same lazy tree and is applied in place
@@ -2111,7 +2129,7 @@
 				</div>
 			{/if}
 		{:else if treeView}
-			<div class="border rounded-md bg-surface-tertiary">
+			<div class="border rounded-md bg-surface-tertiary" style={tableStyle}>
 				{@render tableHeader()}
 				<!-- Remount the tree on a MODE change only (treeKey = view/owner/search/label):
 			     expanded folders (their `opened` state is local to each TreeView) collapse
@@ -2147,13 +2165,17 @@
 				{/key}
 			</div>
 		{:else}
-			<div class="border rounded-md bg-surface-tertiary" class:wm-imported={justImported}>
+			<div
+				class="border rounded-md bg-surface-tertiary"
+				class:wm-imported={justImported}
+				style={tableStyle}
+			>
 				{@render tableHeader()}
 				{#if filter === ''}
 					{#each [...visiblePipelineFolders].sort() as folder (folder)}
 						<a
 							href="{base}/pipeline/{encodeURIComponent(folder)}"
-							class="w-full inline-flex items-center gap-4 pl-5 pr-3 py-2 rounded-md hover:bg-surface-hover transition-colors text-sm"
+							class="w-full inline-flex items-center gap-4 pl-5 pr-3 py-2 {HOME_TABLE_ROW_SEPARATOR} hover:bg-surface-hover transition-colors text-sm"
 						>
 							<NetworkIcon size={16} class="text-emerald-600 dark:text-emerald-400" />
 							<span class="text-xs font-medium text-emphasis truncate">Pipeline · f/{folder}</span>
diff --git a/frontend/src/lib/components/home/RunnableActivityCells.svelte b/frontend/src/lib/components/home/RunnableActivityCells.svelte
index 17b809b04d..b7ab0d9cba 100644
--- a/frontend/src/lib/components/home/RunnableActivityCells.svelte
+++ b/frontend/src/lib/components/home/RunnableActivityCells.svelte
@@ -6,6 +6,9 @@
 	import { displayDate, formatCron } from '$lib/utils'
 	import { describeSchedule } from '$lib/utils/describeCron'
 	import { twMerge } from 'tailwind-merge'
+	import { ExternalLink } from 'lucide-svelte'
+	import { Button } from '$lib/components/common'
+	import { workspaceStore } from '$lib/stores'
 	import { getHomeActivity, type ActivityKind } from './homeActivity.svelte'
 
 	interface Props {
@@ -88,10 +91,11 @@
 {#if homeActivity}
 	<div class="relative z-[1] hidden lg:flex items-center w-24 min-w-0 shrink-0 text-xs">
 		{#if lastRun}
-			<Tooltip class="min-w-0">
-				<a
-					href="{base}/runs/{path}"
-					class="flex items-center gap-1.5 min-w-0 text-secondary hover:text-primary"
+			<!-- The close delay lets the pointer cross into the popup to click a run. -->
+			<Tooltip class="min-w-0" closeDelay={150}>
+				<!-- Not a link: the popover's "View runs" and run entries are the ways in. -->
+				<span
+					class="flex items-center gap-1.5 min-w-0 text-secondary cursor-default"
 					aria-label="Latest runs"
 				>
 					<span class={twMerge('w-1.5 h-1.5 rounded-full shrink-0', statusClass[lastRun.status])}
@@ -103,16 +107,29 @@
 							<TimeAgo date={lastRun.created_at} compact /> ago
 						{/if}
 					</span>
-				</a>
+				</span>
 				{#snippet text()}
-					<div class="flex flex-col gap-1">
-						<span class="font-semibold">Latest {runs.length} runs</span>
+					<div class="flex flex-col gap-1 min-w-56">
+						<div class="flex items-center justify-between gap-4">
+							<span class="font-semibold">Latest {runs.length} runs</span>
+							<Button
+								variant="subtle"
+								unifiedSize="xs"
+								href="{base}/runs/{path}?workspace={$workspaceStore}"
+							>
+								View runs
+							</Button>
+						</div>
 						{#each runs as run (run.id)}
-							<div class="flex items-center gap-2">
+							<a
+								href="{base}/run/{run.id}?workspace={$workspaceStore}"
+								class="group/run -mx-1.5 px-1.5 py-0.5 rounded flex items-center gap-2 text-primary hover:bg-surface-hover"
+							>
 								<div class={twMerge('w-2 h-2 rounded-full', statusClass[run.status])}></div>
 								<span class="w-16">{statusLabel[run.status]}</span>
-								<span class="text-hint">{displayDate(run.created_at, true)}</span>
-							</div>
+								<span class="text-hint grow">{displayDate(run.created_at, true)}</span>
+								<ExternalLink size={12} class="text-hint group-hover/run:text-primary shrink-0" />
+							</a>
 						{/each}
 					</div>
 				{/snippet}
diff --git a/frontend/src/lib/components/home/TreeView.svelte b/frontend/src/lib/components/home/TreeView.svelte
index e5f9531308..f195a34c89 100644
--- a/frontend/src/lib/components/home/TreeView.svelte
+++ b/frontend/src/lib/components/home/TreeView.svelte
@@ -7,7 +7,7 @@
 	import Item from './Item.svelte'
 	import { countLeaves, type FolderItem, type ItemType, type UserItem } from './treeViewUtils'
 	import { twMerge } from 'tailwind-merge'
-	import { isHomeTable } from './homeTable'
+	import { HOME_TABLE_ROW_SEPARATOR, isHomeTable } from './homeTable'
 	import { pluralize } from '$lib/utils'
 	import { base } from '$lib/base'
 	import { Button } from '$lib/components/common'
@@ -74,7 +74,9 @@
 	}: Props = $props()
 
 	// The home table draws no separators between its rows.
-	const separator = isHomeTable() ? 'pl-5 rounded-md hover:bg-surface-hover' : 'border-b'
+	const separator = isHomeTable()
+		? `pl-5 hover:bg-surface-hover ${HOME_TABLE_ROW_SEPARATOR}`
+		: 'border-b'
 
 	let visualDepth = $derived(depth + indent)
 
diff --git a/frontend/src/lib/components/home/TreeViewRoot.svelte b/frontend/src/lib/components/home/TreeViewRoot.svelte
index b959a1c56a..38fa5ece28 100644
--- a/frontend/src/lib/components/home/TreeViewRoot.svelte
+++ b/frontend/src/lib/components/home/TreeViewRoot.svelte
@@ -1,4 +1,5 @@
 <script lang="ts">
+	import { HOME_TABLE_ROW_SEPARATOR } from './homeTable'
 	import { untrack, type Snippet } from 'svelte'
 	import TreeView from './TreeView.svelte'
 	import { countLeaves, groupItems, type ItemType, type UserItem } from './treeViewUtils'
@@ -287,7 +288,7 @@
 					<!-- svelte-ignore a11y_no_static_element_interactions -->
 					<div
 						onclick={toggleOtherUsers}
-						class="pl-5 pr-3 py-2 rounded-md hover:bg-surface-hover w-full flex flex-row items-center justify-between cursor-pointer"
+						class="pl-5 pr-3 py-2 hover:bg-surface-hover {HOME_TABLE_ROW_SEPARATOR} w-full flex flex-row items-center justify-between cursor-pointer"
 					>
 						<div class="flex flex-row items-center gap-4">
 							<Users size={16} class="text-secondary" />
diff --git a/frontend/src/lib/components/home/homeTable.ts b/frontend/src/lib/components/home/homeTable.ts
index c2dd5eb3bd..443a693090 100644
--- a/frontend/src/lib/components/home/homeTable.ts
+++ b/frontend/src/lib/components/home/homeTable.ts
@@ -7,12 +7,19 @@ import { getContext, setContext } from 'svelte'
  * triggers and runs cells are hidden, and the template drops them too.
  */
 export const HOME_TABLE_GRID =
-	'grid items-center gap-x-5 grid-cols-[1rem_minmax(0,1fr)_6.5rem] lg:grid-cols-[1rem_minmax(0,2fr)_minmax(0,1.5fr)_6rem_13rem_5rem_6.5rem]'
+	'grid items-center gap-x-5 grid-cols-[1rem_minmax(0,1fr)_var(--home-actions-w,6.5rem)] lg:grid-cols-[1rem_minmax(0,3fr)_minmax(0,1fr)_6rem_13rem_5rem_var(--home-actions-w,6.5rem)]'
+
+/** Actions column width when some row shows "Edit in fork" instead of Edit. */
+export const HOME_TABLE_WIDE_ACTIONS = '--home-actions-w: 12.5rem'
 
 /** Sub-columns of the badges area: labels · shared. */
 export const HOME_TABLE_BADGE_GRID =
 	'grid-cols-[minmax(0,1fr)_1.25rem] gap-x-2 items-center min-w-0'
 
+/** The faint line between home table rows; the last row in the box draws none. */
+export const HOME_TABLE_ROW_SEPARATOR =
+	'border-b border-gray-100 dark:border-gray-700/40 last:border-b-0'
+
 /** Shows a muted dash in a table cell that renders no element. */
 export const EMPTY_CELL_DASH =
 	"[&:not(:has(*))]:after:content-['–'] [&:not(:has(*))]:after:text-hint [&:not(:has(*))]:after:text-2xs [&:not(:has(*))]:after:opacity-40"