Live game move count lives in the snapshot, not the games row

In a Go/real-time-game backend, the persistent games row often stores move_count = 0 until the game ENDS (written once at finish). The live count during play lives in a separate active-game snapshot (moves_json length) or the in-memory live object. REST views that read games.move_count show a stale 0 for in-progress games. Fix: overlay the snapshot count for endedAt==null games. Same trap for last-move time (use the snapshot updated_at, not started_at, to rank live games by recency).