fix(background-agent): track and cancel completion timers to prevent memory leaks

[sisyphus-dev-ai]

Summary

Fixes memory leak in BackgroundManager where completion timers (5-minute delayed cleanup) were not tracked or cancelled on shutdown, causing the manager instance to be held in memory by timer callbacks.

Investigation Summary

Investigated the 6 memory leak patterns mentioned in #1043:

Issue	Status
setTimeout timers (manager.ts:1011-1018)	REAL BUG - FIXED
setInterval polling (manager.ts:790-804)	False positive - already stops when no tasks
session-notification.ts Maps/Sets	False positive - has proper cleanup via maxTrackedSessions
tool-input-cache.ts cache	False positive - has TTL cleanup every 60s
atlas/index.ts pendingFilePaths	Minor - small strings, not worth fixing
context-injector/collector.ts sessions	Minor - consumed during injection

Changes

• Add completionTimers: Map<string, ReturnType<typeof setTimeout>> to track timer IDs
• Store timer reference in notifyParentSession() when scheduling 5-minute cleanup
• Cancel and remove timer when task is deleted via session.deleted event
• Clear all timers in shutdown() method

Testing

• TDD approach: wrote failing tests first, then implemented fix
• 4 new tests covering timer tracking, shutdown cleanup, and session.deleted cleanup
• All 83 background-agent tests pass
• Typecheck passes

Closes #1043

---

Summary by cubic

Fixed a memory leak in BackgroundManager by tracking and cancelling 5-minute completion timers. Timers are now canceled on shutdown and when tasks are deleted, preventing the manager from being kept in memory (fixes #1043).

• Bug Fixes
  • Added a completionTimers Map to track setTimeout handles.
  • Stored timers in notifyParentSession; cancel and remove on session.deleted.
  • Cleared all timers in shutdown to avoid leaks.

^{Written for commit 9e260ed. Summary will update on new commits.}

[cubic-dev-ai]

No issues found across 2 files

Confidence score: 5/5

• Automated review surfaced no issues in the provided summaries.
• No files require special attention.