Summary

• Fix pollRunningTasks() in BackgroundManager to handle undefined sessionStatus (when completed sessions are no longer in the status response)
• Match the sync-session-poller pattern: only skip completion check when status EXISTS and is not idle; when undefined, fall through to completion detection
• Add 3 tests covering undefined, idle, and busy sessionStatus scenarios

Root Cause

When session.status() stops returning a completed session, allStatuses[sessionID] is undefined. The old code only handled idle explicitly, treating undefined as "still running" — which left the task stuck in running status forever.

Fix

Restructured the control flow in pollRunningTasks():

1. Check retry first (preserve existing retry handling)
2. Use inverse logic: if (sessionStatus && sessionStatus.type !== "idle") { continue } — only continue if status exists AND is not idle
3. Fall through to validateSessionHasOutput + checkSessionTodos + tryCompleteTask for both idle AND undefined cases

This matches the pattern already used in sync-session-poller.ts:75.

Closes #2387

Summary by cubic

Fixes background task polling so a missing session status no longer leaves tasks stuck in "running". Matches sync-session-poller behavior and adds tests for undefined, idle, and busy states.

• Bug Fixes
  • Update pollRunningTasks() in BackgroundManager to handle undefined sessionStatus by running completion checks (validate output, check todos, then complete).
  • Only skip completion when status exists and is not idle; keep retry handling and improve logs.
  • Add tests covering undefined, idle, and busy session status scenarios.

^{Written for commit dc370f7. Summary will update on new commits.}