- Add a shared AiSessionSync store with BroadcastChannel + storage fallback, ownership locks, heartbeats, and stale-tab detection
- Merge cross-tab session snapshots into useBackgroundSessions with timestamp guards and rebroadcast SSE updates to peers
- Update background session UI and planning/mission/subtask modals to show active-tab lock status and only allow takeover when ownership is stale
- Add hook tests covering sync store messaging/fallback behavior and background session cross-tab merge flows
