refactor(worktree): split background pane exit-output recording out

The sequenced-command fix pushed launch-worktree-background-terminals.ts
to 303 effective lines, over the 300 cap. Moved persistExitedPaneOutput
and registerBackgroundPaneBuffer, which are one concern, into
background-pane-exit-output.ts. No behavior change: dropping the
registerEagerPtyBuffer call still reddens the background-terminals suite.

src/renderer/src/lib/background-pane-exit-output.ts

@@ -0,0 +1,49 @@
+import {
+  registerEagerPtyBuffer,
+  type EagerPtyHandle
+} from '@/components/terminal-pane/pty-dispatcher'
+import { useAppStore } from '@/store'
+
+/** The id a background pane got, plus which lifetime of it this spawn owns. */
+export type SpawnedPane = { ptyId: string; incarnationId?: string }
+
+function persistExitedPaneOutput(tabId: string, leafId: string, output: string): void {
+  const store = useAppStore.getState()
+  const layout = store.terminalLayoutsByTabId[tabId]
+  if (!layout) {
+    return
+  }
+  const { ptyIdsByLeafId: existingPtyIds, buffersByLeafId: existingBuffers, ...rest } = layout
+  const nextPtyIds = { ...existingPtyIds }
+  delete nextPtyIds[leafId]
+  const trimmedOutput = output.trim() ? output : ''
+  store.setTabLayout(tabId, {
+    ...rest,
+    ...(Object.keys(nextPtyIds).length > 0 ? { ptyIdsByLeafId: nextPtyIds } : {}),
+    ...(trimmedOutput
+      ? {
+          buffersByLeafId: {
+            ...existingBuffers,
+            [leafId]: output
+          }
+        }
+      : existingBuffers
+        ? { buffersByLeafId: existingBuffers }
+        : {})
+  })
+}
+
+// Why the incarnation: a relay-recycled id can hold the previous owner's exit, and draining that
+// into this handler tears the pane down seconds after it launched.
+export function registerBackgroundPaneBuffer(
+  tabId: string,
+  leafId: string,
+  pane: SpawnedPane
+): void {
+  let eagerBuffer: EagerPtyHandle | null = null
+  const onExit = (exitPtyId: string): void => {
+    persistExitedPaneOutput(tabId, leafId, eagerBuffer?.flush() ?? '')
+    useAppStore.getState().clearTabPtyId(tabId, exitPtyId)
+  }
+  eagerBuffer = registerEagerPtyBuffer(pane.ptyId, onExit, pane.incarnationId)
+}

src/renderer/src/lib/launch-worktree-background-terminals.ts

@@ -1,7 +1,4 @@
-import {
-  registerEagerPtyBuffer,
-  type EagerPtyHandle
-} from '@/components/terminal-pane/pty-dispatcher'
+import { registerBackgroundPaneBuffer, type SpawnedPane } from '@/lib/background-pane-exit-output'
 import { createBrowserUuid } from '@/lib/browser-uuid'
 import { getSettingsForWorktreeRuntimeOwner } from '@/lib/worktree-runtime-owner'
 import { getActiveRuntimeTarget } from '@/runtime/runtime-rpc-client'
@@ -87,43 +84,6 @@ function buildSplitLayout(
   }
 }
 
-function persistExitedPaneOutput(tabId: string, leafId: string, output: string): void {
-  const store = useAppStore.getState()
-  const layout = store.terminalLayoutsByTabId[tabId]
-  if (!layout) {
-    return
-  }
-  const { ptyIdsByLeafId: existingPtyIds, buffersByLeafId: existingBuffers, ...rest } = layout
-  const nextPtyIds = { ...existingPtyIds }
-  delete nextPtyIds[leafId]
-  const trimmedOutput = output.trim() ? output : ''
-  store.setTabLayout(tabId, {
-    ...rest,
-    ...(Object.keys(nextPtyIds).length > 0 ? { ptyIdsByLeafId: nextPtyIds } : {}),
-    ...(trimmedOutput
-      ? {
-          buffersByLeafId: {
-            ...existingBuffers,
-            [leafId]: output
-          }
-        }
-      : existingBuffers
-        ? { buffersByLeafId: existingBuffers }
-        : {})
-  })
-}
-
-// Why the incarnation: a relay-recycled id can hold the previous owner's exit, and draining that
-// into this handler tears the pane down seconds after it launched.
-function registerBackgroundPaneBuffer(tabId: string, leafId: string, pane: SpawnedPane): void {
-  let eagerBuffer: EagerPtyHandle | null = null
-  const onExit = (exitPtyId: string): void => {
-    persistExitedPaneOutput(tabId, leafId, eagerBuffer?.flush() ?? '')
-    useAppStore.getState().clearTabPtyId(tabId, exitPtyId)
-  }
-  eagerBuffer = registerEagerPtyBuffer(pane.ptyId, onExit, pane.incarnationId)
-}
-
 function buildSetupCommand(setup: WorktreeSetupLaunch): string {
   // Why: a sequenced launch carries the gated command that records setup's outcome for a waiting
   // agent terminal; rebuilding the bare runner here ran setup but recorded nothing, so the agent
@@ -139,9 +99,6 @@ function buildSetupCommand(setup: WorktreeSetupLaunch): string {
   )
 }
 
-/** The id a background pane got, plus which lifetime of it this spawn owns. */
-type SpawnedPane = { ptyId: string; incarnationId?: string }
-
 async function spawnPane(args: {
   worktree: Worktree
   connectionId: string | null