- Games record start and move times, spectator peak and distinct count
- Games end as completed, left (the leaver loses), timeout (5 minutes
offline on your turn while the opponent is online) or inactive (both
offline for 30 minutes); everyone gets on_game_end
- Connection info carries offlineSince for the countdown
- A new game is rejected while the user has one in progress
- Live games are written to Valkey after every change and restored on
startup; finished games are saved to Postgres with public ids, and
saves that fail are kept and retried every 30 seconds
- Clients get a trimmed game without spectator ids
- Startup waits for Valkey, restores games, then accepts connections;
migrations are retried while Postgres is unreachable
