diff --git a/frontend/src/lib/components/common/tabs/Tab.svelte b/frontend/src/lib/components/common/tabs/Tab.svelte
index a652525b45..edb1135bbc 100644
--- a/frontend/src/lib/components/common/tabs/Tab.svelte
+++ b/frontend/src/lib/components/common/tabs/Tab.svelte
@@ -99,6 +99,7 @@
 	}}
 	{disabled}
 	{id}
+	data-tab-selected={isSelected ? 'true' : undefined}
 >
 	<div
 		class={twMerge(
diff --git a/frontend/src/lib/components/common/tabs/Tabs.svelte b/frontend/src/lib/components/common/tabs/Tabs.svelte
index 65daedf622..158706c5ad 100644
--- a/frontend/src/lib/components/common/tabs/Tabs.svelte
+++ b/frontend/src/lib/components/common/tabs/Tabs.svelte
@@ -25,6 +25,15 @@
 		 * Use this when you want to prevent navigation before checking for unsaved changes.
 		 */
 		deferSelectedUpdate?: boolean
+		/**
+		 * Draw the selection as one bar that slides between tabs, rather than a border each tab
+		 * turns on. Opt-in, so every existing strip keeps the border it has: a strip whose tabs
+		 * appear as their content does needs the move to be visible, and a border cannot travel.
+		 * Tabs keep their own bottom border unless the caller turns it off.
+		 */
+		slidingIndicator?: boolean
+		/** Colour of that bar. */
+		indicatorClass?: string
 	}
 
 	let {
@@ -37,7 +46,9 @@
 		values = undefined,
 		children,
 		content,
-		deferSelectedUpdate = false
+		deferSelectedUpdate = false,
+		slidingIndicator = false,
+		indicatorClass = 'bg-border-normal'
 	}: Props = $props()
 
 	// Single source of truth for tab state
@@ -61,6 +72,45 @@
 		selectedStore.set(selected)
 	})
 
+	// Measured off the selected Tab rather than tracked in state: a Tab decides on its own
+	// whether it is selected (prefix and otherValues matching), and its width is whatever its
+	// label renders to. Zero width means nothing is selected yet, and the bar stays hidden.
+	let row: HTMLDivElement | undefined = $state()
+	let bar = $state({ x: 0, w: 0 })
+
+	function measureBar() {
+		const el = row?.querySelector<HTMLElement>('[data-tab-selected="true"]')
+		bar = el ? { x: el.offsetLeft, w: el.offsetWidth } : { x: bar.x, w: 0 }
+	}
+
+	// Placing the bar for the first paint. Every later move comes from the observers below: a
+	// Tab marks itself selected in its own update, which has not run when an effect here does,
+	// so measuring from this side alone lands the bar on the tab that was selected before.
+	$effect(() => {
+		if (!slidingIndicator) return
+		void row
+		measureBar()
+	})
+
+	$effect(() => {
+		if (!slidingIndicator || !row) return
+		const ro = new ResizeObserver(measureBar)
+		ro.observe(row)
+		// The mark moving is the selection changing; a tab added or removed, or one that grows a
+		// count as its content arrives, changes what the bar has to sit on.
+		const mo = new MutationObserver(measureBar)
+		mo.observe(row, {
+			childList: true,
+			subtree: true,
+			attributes: true,
+			attributeFilter: ['data-tab-selected']
+		})
+		return () => {
+			ro.disconnect()
+			mo.disconnect()
+		}
+	})
+
 	let hashValues = $derived(values ? values.map((x) => '#' + x) : undefined)
 
 	function hashChange() {
@@ -79,8 +129,26 @@
 	<ScrollableX class={wrapperClass}>
 		<!-- `scrollbar-hidden` is inert on this non-scrolling row (ScrollableX owns the
 			 scroll), but TroubleshootFlowTutorial targets it as a selector hook — keep it. -->
-		<div class={twMerge('border-b flex flex-row whitespace-nowrap scrollbar-hidden', c)} {style}>
+		<div
+			bind:this={row}
+			class={twMerge(
+				'border-b flex flex-row whitespace-nowrap scrollbar-hidden',
+				slidingIndicator ? 'relative' : '',
+				c
+			)}
+			{style}
+		>
 			{@render children?.({ selected })}
+			{#if slidingIndicator}
+				<span
+					aria-hidden="true"
+					class={twMerge(
+						'pointer-events-none absolute -bottom-px h-0.5 rounded-t-sm transition-[transform,width,opacity] duration-200 ease-out motion-reduce:transition-none',
+						indicatorClass
+					)}
+					style={`left:0; width:${bar.w}px; transform:translateX(${bar.x}px); opacity:${bar.w ? 1 : 0}`}
+				></span>
+			{/if}
 		</div>
 	</ScrollableX>
 {/if}
diff --git a/frontend/src/lib/components/copilot/chat/RunScriptCard.svelte b/frontend/src/lib/components/copilot/chat/RunScriptCard.svelte
index 4ae3cc9b3d..23e66e7d43 100644
--- a/frontend/src/lib/components/copilot/chat/RunScriptCard.svelte
+++ b/frontend/src/lib/components/copilot/chat/RunScriptCard.svelte
@@ -1,4 +1,7 @@
 <script lang="ts">
+	import { onMount } from 'svelte'
+	import { cubicOut } from 'svelte/easing'
+	import { prefersReducedMotion } from 'svelte/motion'
 	import { Ban, Loader2, TimerOff } from 'lucide-svelte'
 	import { twMerge } from 'tailwind-merge'
 	import { Button, Tab, Tabs } from '$lib/components/common'
@@ -136,6 +139,34 @@
 		pending && (aiChatManager.isRunFormInPreview?.(message.tool_call_id) ?? false)
 	)
 
+	// The three moments a run moves the card — a tab arrives, the selection follows it, the body
+	// changes under it — used to land in one frame each, which is why the card was hard to follow.
+	// A tab already on screen when the card mounts never arrived, so a settled call restored from
+	// history renders its strip at rest.
+	let liveStrip = $state(false)
+	onMount(() => (liveStrip = true))
+
+	function growIn(node: HTMLElement, { live }: { live: boolean }) {
+		const width = node.getBoundingClientRect().width
+		return {
+			duration: live && !prefersReducedMotion.current ? 170 : 0,
+			easing: cubicOut,
+			css: (t: number) => `width:${t * width}px; opacity:${t}`
+		}
+	}
+
+	/** The body fades in over the time the bar takes to travel, so the two halves of a tab change
+	 * land together rather than one instantly and one over 200ms. No shift with it: the logs open
+	 * pinned to the end of their own scroll, which clips one, and a pane that moves on two tabs
+	 * out of three reads as a glitch rather than as direction. */
+	function enterPane(_node: HTMLElement) {
+		return {
+			duration: liveStrip && !prefersReducedMotion.current ? 200 : 0,
+			easing: cubicOut,
+			css: (t: number) => `opacity:${t}`
+		}
+	}
+
 	let bodyEl: HTMLDivElement | undefined = $state()
 
 	const fades = scrollFades()
@@ -303,22 +334,29 @@
 				on:selected={(e) => (userTab = e.detail)}
 				class="h-8 px-3 font-main"
 				wrapperClass="shrink-0"
+				slidingIndicator
+				indicatorClass="bg-border-accent"
 			>
 				{#if !jsonView}
 					{#each tabs as tab (tab.value)}
-						<Tab
-							value={tab.value}
-							label={tab.label}
-							class="py-0.5 text-2xs font-medium leading-4 text-secondary"
-							selectedClass="text-accent border-border-accent"
-							exact
-						>
-							{#snippet extra()}
-								{#if tab.value === 'logs' && logLineCount > 0}
-									<span class="text-2xs text-hint">{logLineCount}</span>
-								{/if}
-							{/snippet}
-						</Tab>
+						<!-- The tab widens in first and the bar follows it, because a run adds its tabs as
+						     it produces them: landing the selection on a tab in the frame it appears reads
+						     as one unexplained jump. `border-b-0` because the bar is the selection now. -->
+						<span class="inline-flex overflow-hidden" in:growIn={{ live: liveStrip }}>
+							<Tab
+								value={tab.value}
+								label={tab.label}
+								class="border-b-0 py-0.5 text-2xs font-medium leading-4 text-secondary"
+								selectedClass="text-accent"
+								exact
+							>
+								{#snippet extra()}
+									{#if tab.value === 'logs' && logLineCount > 0}
+										<span class="text-2xs text-hint">{logLineCount}</span>
+									{/if}
+								{/snippet}
+							</Tab>
+						</span>
 					{/each}
 				{/if}
 				<div class="ml-auto flex items-center pl-2">
@@ -358,78 +396,89 @@
 								showFade
 							/>
 						</div>
-					{:else if activeTab === 'input'}
-						<!-- What the runs page shows a finished job's arguments as: the operator has already
+					{:else}
+						<!-- Keyed on the tab so the body arrives rather than cuts. One region serves every
+						     tab, so only the incoming pane moves: overlapping them would ask this scroller
+						     to hold two at once. -->
+						{#key activeTab}
+							<div class="flex min-h-full flex-1 flex-col" in:enterPane>
+								{#if activeTab === 'input'}
+									<!-- What the runs page shows a finished job's arguments as: the operator has already
 					     read this table. The job id is what lets it fetch arguments too big to have been
 					     persisted with the card. -->
-						<JobArgs
-							args={parameters}
-							id={chatJob?.jobId}
-							workspace={chatJob?.workspace}
-							disableExpand
-						/>
-					{:else if activeTab === 'logs'}
-						{#if logs.trim()}
-							{#if logs.length >= MAX_LOG_LENGTH}
-								<p class="mb-1 text-2xs text-tertiary">
-									Tail of the logs, the last {MAX_LOG_LENGTH} characters.
-								</p>
-							{/if}
-							<pre class="whitespace-pre-wrap break-words font-mono text-2xs text-primary"
-								>{logs}</pre
-							>
-						{:else}
-							<p class="text-2xs text-tertiary">No logs yet.</p>
-						{/if}
-						{#if running}
-							<div class="mt-1 flex items-center gap-1.5 text-2xs text-tertiary">
-								<Loader2 class="h-3 w-3 animate-spin" />
-								streaming
-							</div>
-						{/if}
-					{:else if failed}
-						<pre
-							class="whitespace-pre-wrap break-words font-mono text-2xs text-red-700 dark:text-red-300"
-							>{message.error}</pre
-						>
-					{:else if streaming}
-						<!-- The same renderer as a landed result, handed the partial: it is the one that
+									<JobArgs
+										args={parameters}
+										id={chatJob?.jobId}
+										workspace={chatJob?.workspace}
+										disableExpand
+									/>
+								{:else if activeTab === 'logs'}
+									{#if logs.trim()}
+										{#if logs.length >= MAX_LOG_LENGTH}
+											<p class="mb-1 text-2xs text-tertiary">
+												Tail of the logs, the last {MAX_LOG_LENGTH} characters.
+											</p>
+										{/if}
+										<pre class="whitespace-pre-wrap break-words font-mono text-2xs text-primary"
+											>{logs}</pre
+										>
+									{:else}
+										<p class="text-2xs text-tertiary">No logs yet.</p>
+									{/if}
+									{#if running}
+										<div class="mt-1 flex items-center gap-1.5 text-2xs text-tertiary">
+											<Loader2 class="h-3 w-3 animate-spin" />
+											streaming
+										</div>
+									{/if}
+								{:else if failed}
+									<pre
+										class="whitespace-pre-wrap break-words font-mono text-2xs text-red-700 dark:text-red-300"
+										>{message.error}</pre
+									>
+								{:else if streaming}
+									<!-- The same renderer as a landed result, handed the partial: it is the one that
 					     knows how to show a result arriving in pieces. -->
-						<DisplayResult
-							result={undefined}
-							result_stream={resultStream}
-							jobId={chatJob?.jobId}
-							workspaceId={chatJob?.workspace}
-							disableExpand
-							hideAsJson
-						/>
-					{:else if resultValue !== undefined}
-						<!-- The run page's own renderer, not a second one invented for the chat: it handles
+									<DisplayResult
+										result={undefined}
+										result_stream={resultStream}
+										jobId={chatJob?.jobId}
+										workspaceId={chatJob?.workspace}
+										disableExpand
+										hideAsJson
+									/>
+								{:else if resultValue !== undefined}
+									<!-- The run page's own renderer, not a second one invented for the chat: it handles
 					     markdown, tables, images and deep nesting without the card guessing at the
 					     shape, and reaches the job through jobId/workspace for an S3 preview.
 					     `disableExpand` drops its toolbar and `hideAsJson` its Pretty/JSON switch,
 					     which the row already owns. -->
-						<DisplayResult
-							result={resultValue}
-							jobId={chatJob?.jobId}
-							workspaceId={chatJob?.workspace}
-							disableExpand
-							hideAsJson
-						/>
-					{:else if canceled}
-						<!-- All that is left to render is the fact itself: a form cancelled before Run
+									<DisplayResult
+										result={resultValue}
+										jobId={chatJob?.jobId}
+										workspaceId={chatJob?.workspace}
+										disableExpand
+										hideAsJson
+									/>
+								{:else if canceled}
+									<!-- All that is left to render is the fact itself: a form cancelled before Run
 						     never reached a job, so there is no result the way a cancelled run has one. -->
-						<div class="flex flex-1 flex-col items-center justify-center gap-1.5 px-4 text-center">
-							<Ban class="h-4 w-4 text-tertiary" />
-							<p class="text-2xs font-medium leading-4 text-secondary">{cancelReason}</p>
-							{#if !ran}
-								<p class="text-2xs leading-4 text-tertiary">
-									The inputs it would have run with are on the Inputs tab.
-								</p>
-							{/if}
-						</div>
-					{:else}
-						<p class="text-2xs text-tertiary">This run returned no result.</p>
+									<div
+										class="flex flex-1 flex-col items-center justify-center gap-1.5 px-4 text-center"
+									>
+										<Ban class="h-4 w-4 text-tertiary" />
+										<p class="text-2xs font-medium leading-4 text-secondary">{cancelReason}</p>
+										{#if !ran}
+											<p class="text-2xs leading-4 text-tertiary">
+												The inputs it would have run with are on the Inputs tab.
+											</p>
+										{/if}
+									</div>
+								{:else}
+									<p class="text-2xs text-tertiary">This run returned no result.</p>
+								{/if}
+							</div>
+						{/key}
 					{/if}
 				</div>
 			</div>