- Draw offer now syncs: sender sees confirmation, receiver sees
  accept/deny dialog with 30s timeout
- Emotes now show the correct emoji (was hardcoded to 3 mappings,
  now uses actual emote key lookup)
- Emote dedup via timestamp tracking — no repeated display
- game_state is now MERGED server-side instead of overwritten,
  so emotes don't wipe draw offers and vice versa
- Polling runs regardless of whose turn it is (emotes/draws
  need to arrive during your own turn too)
- Draw accept/decline response properly detected by offerer
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>