fix(background-agent): preserve terminal tasks until notification cleanup

[code-yeongyu]

Summary

• keep session.error and session.deleted tasks in memory until the parent notification queue runs, so terminal tasks do not disappear before their result can be surfaced
• move pending-parent cleanup to notification time so simultaneous completions only emit one final all-complete notification
• skip terminal tasks during TTL pruning and cover the regressions with background-agent tests

Testing

• bun test src/features/background-agent/
• bun run typecheck
• bun run build

Closes #2292

---

Summary by cubic

Fixes #2292 by preserving terminal background tasks until the parent notification runs, so results don’t disappear. Cleanup is deferred to notification time and TTL pruning skips terminal tasks.

• Bug Fixes
  • Keep completed/error/cancelled/interrupt tasks in memory until notifyParentSession runs.
  • Defer pendingByParent cleanup to notification time; coalesce simultaneous completions into one final “all complete” notification.
  • Skip terminal tasks during pruneStaleTasksAndNotifications; add tests to cover this.
  • On session.deleted: cancel descendants, remove toast entries, keep tasks until delayed cleanup, and preserve completion timers.

^{Written for commit 3b58828. Summary will update on new commits.}

[cubic-dev-ai]

No issues found across 4 files

Confidence score: 5/5

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

_{Requires human review: Moving cleanup to async notification paths and removing the TTL pruning safety net for terminal tasks could lead to memory leaks if timers or notifications fail to fire.}