- Broadcast game_state_update in game_engine.start_game() so frontend
receives the active state immediately
- Add auto-start safeguard to /lineup-status endpoint for stuck pending
games (both in-memory and database code paths)
- Fix None handling in state_manager._rebuild_state_from_data() for
pending games with null inning/half values
Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>