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/notification-tracker.ts

@@ -0,0 +1,52 @@
+import type { BackgroundTask } from "./types"
+
+export function markForNotification(
+  notifications: Map<string, BackgroundTask[]>,
+  task: BackgroundTask
+): void {
+  const queue = notifications.get(task.parentSessionID) ?? []
+  queue.push(task)
+  notifications.set(task.parentSessionID, queue)
+}
+
+export function getPendingNotifications(
+  notifications: Map<string, BackgroundTask[]>,
+  sessionID: string
+): BackgroundTask[] {
+  return notifications.get(sessionID) ?? []
+}
+
+export function clearNotifications(
+  notifications: Map<string, BackgroundTask[]>,
+  sessionID: string
+): void {
+  notifications.delete(sessionID)
+}
+
+export function clearNotificationsForTask(
+  notifications: Map<string, BackgroundTask[]>,
+  taskId: string
+): void {
+  for (const [sessionID, tasks] of notifications.entries()) {
+    const filtered = tasks.filter((t) => t.id !== taskId)
+    if (filtered.length === 0) {
+      notifications.delete(sessionID)
+    } else {
+      notifications.set(sessionID, filtered)
+    }
+  }
+}
+
+export function cleanupPendingByParent(
+  pendingByParent: Map<string, Set<string>>,
+  task: BackgroundTask
+): void {
+  if (!task.parentSessionID) return
+  const pending = pendingByParent.get(task.parentSessionID)
+  if (!pending) return
+
+  pending.delete(task.id)
+  if (pending.size === 0) {
+    pendingByParent.delete(task.parentSessionID)
+  }
+}