WIP: Add multiplayer Snake game

N-player (2-8) real-time Snake game alongside Connect 4.
Lobby has tabs to switch between games. Players join via
invite link with 10-second countdown. Game loop runs at
tick-based intervals with NATS pub/sub for state sync.

Keyboard input not yet working (Datastar keydown binding
issue still under investigation).

db/queries/games.sql

@@ -15,7 +15,7 @@ WHERE id = ?;
 DELETE FROM games WHERE id = ?;
 
 -- name: GetActiveGames :many
-SELECT * FROM games WHERE status < 2;
+SELECT * FROM games WHERE game_type = 'connect4' AND status < 2;
 
 -- name: CreateGamePlayer :exec
 INSERT INTO game_players (game_id, user_id, guest_player_id, nickname, color, slot)
@@ -41,5 +41,5 @@ SELECT
 FROM games g
 JOIN game_players gp_user ON g.id = gp_user.game_id AND gp_user.user_id = ?
 LEFT JOIN game_players gp_opponent ON g.id = gp_opponent.game_id AND gp_opponent.slot != gp_user.slot
-WHERE g.status < 2
+WHERE g.game_type = 'connect4' AND g.status < 2
 ORDER BY g.updated_at DESC;