refactor(background-agent): split manager.ts into focused modules

Extract 30+ single-responsibility modules from manager.ts (1556 LOC):
- task lifecycle: task-starter, task-completer, task-canceller, task-resumer
- task queries: task-queries, task-poller, task-queue-processor
- notifications: notification-builder, notification-tracker, parent-session-notifier
- session handling: session-validator, session-output-validator, session-todo-checker
- spawner: spawner/ directory with focused spawn modules
- utilities: duration-formatter, error-classifier, message-storage-locator
- result handling: result-handler-context, background-task-completer
- shutdown: background-manager-shutdown, process-signal

src/features/background-agent/stale-task-pruner.ts

@@ -0,0 +1,57 @@
+import { log } from "../../shared"
+
+import { TASK_TTL_MS } from "./constants"
+import { subagentSessions } from "../claude-code-session-state"
+import { pruneStaleTasksAndNotifications } from "./task-poller"
+
+import type { BackgroundTask } from "./types"
+import type { ConcurrencyManager } from "./concurrency"
+
+export function pruneStaleState(args: {
+  tasks: Map<string, BackgroundTask>
+  notifications: Map<string, BackgroundTask[]>
+  concurrencyManager: ConcurrencyManager
+  cleanupPendingByParent: (task: BackgroundTask) => void
+  clearNotificationsForTask: (taskId: string) => void
+}): void {
+  const {
+    tasks,
+    notifications,
+    concurrencyManager,
+    cleanupPendingByParent,
+    clearNotificationsForTask,
+  } = args
+
+  pruneStaleTasksAndNotifications({
+    tasks,
+    notifications,
+    onTaskPruned: (taskId, task, errorMessage) => {
+      const now = Date.now()
+      const timestamp = task.status === "pending"
+        ? task.queuedAt?.getTime()
+        : task.startedAt?.getTime()
+      const age = timestamp ? now - timestamp : TASK_TTL_MS
+
+      log("[background-agent] Pruning stale task:", {
+        taskId,
+        status: task.status,
+        age: Math.round(age / 1000) + "s",
+      })
+
+      task.status = "error"
+      task.error = errorMessage
+      task.completedAt = new Date()
+      if (task.concurrencyKey) {
+        concurrencyManager.release(task.concurrencyKey)
+        task.concurrencyKey = undefined
+      }
+
+      cleanupPendingByParent(task)
+      clearNotificationsForTask(taskId)
+      tasks.delete(taskId)
+      if (task.sessionID) {
+        subagentSessions.delete(task.sessionID)
+      }
+    },
+  })
+}