fix: prevent stale timeout from killing actively running background tasks

The stale detection was checking lastUpdate timestamps BEFORE
consulting session.status(), causing tasks to be unfairly killed
after 3 minutes even when the session was actively running
(e.g., during long tool executions or extended thinking).

Changes:
- Reorder pollRunningTasks to fetch session.status() before stale check
- Skip stale-kill entirely when session status is 'running'
- Port no-lastUpdate handling from task-poller.ts into manager.ts
  (previously manager silently skipped tasks without lastUpdate)
- Add sessionStatuses parameter to checkAndInterruptStaleTasks
- Add 7 new test cases covering session-status-aware stale detection

src/features/background-agent/poll-running-tasks.ts

@@ -34,7 +34,7 @@ export async function pollRunningTasks(args: {
   tasks: Iterable<BackgroundTask>
   client: OpencodeClient
   pruneStaleTasksAndNotifications: () => void
-  checkAndInterruptStaleTasks: () => Promise<void>
+  checkAndInterruptStaleTasks: (statuses: Record<string, { type: string }>) => Promise<void>
   validateSessionHasOutput: (sessionID: string) => Promise<boolean>
   checkSessionTodos: (sessionID: string) => Promise<boolean>
   tryCompleteTask: (task: BackgroundTask, source: string) => Promise<boolean>
@@ -54,11 +54,12 @@ export async function pollRunningTasks(args: {
   } = args
 
   pruneStaleTasksAndNotifications()
-  await checkAndInterruptStaleTasks()
 
   const statusResult = await client.session.status()
   const allStatuses = ((statusResult as { data?: unknown }).data ?? {}) as SessionStatusMap
 
+  await checkAndInterruptStaleTasks(allStatuses)
+
   for (const task of tasks) {
     if (task.status !== "running") continue