fix(server): winner_id on completed games + stats idempotency latch

Two issues in the GAME_OVER broadcast path:

1. log_game_end called update_game_completed with winner_id=None default,
   so games_v2.winner_id was NULL on all 17 completed staging rows. The
   denormalized column existed but carried no information. Compute winner
   (lowest total; None on tie) in broadcast_game_state and thread through.

2. _process_stats_safe had no idempotency guard. log_game_end was already
   self-guarding via game_log_id=None after first fire, but nothing
   stopped repeated GAME_OVER broadcasts from re-firing stats and
   double-counting games_played/games_won. Add Room.stats_processed latch;
   reset it in handle_start_game so a re-used room still records.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

server/handlers.py

@@ -209,6 +209,8 @@ async def handle_start_game(data: dict, ctx: ConnectionContext, *, broadcast_gam
 
     async with ctx.current_room.game_lock:
         ctx.current_room.game.start_game(num_decks, num_rounds, options)
+        # Reset the per-game idempotency latch so this game's stats can fire.
+        ctx.current_room.stats_processed = False
 
         game_logger = get_logger()
         if game_logger: