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;

db/queries/snake_games.sql

@@ -0,0 +1,37 @@
+-- name: CreateSnakeGame :one
+INSERT INTO games (id, board, current_turn, status, game_type, grid_width, grid_height, max_players)
+VALUES (?, ?, 0, ?, 'snake', ?, ?, 8)
+RETURNING *;
+
+-- name: GetSnakeGame :one
+SELECT * FROM games WHERE id = ? AND game_type = 'snake';
+
+-- name: UpdateSnakeGame :exec
+UPDATE games
+SET board = ?, status = ?, winner_user_id = ?, rematch_game_id = ?, updated_at = CURRENT_TIMESTAMP
+WHERE id = ? AND game_type = 'snake';
+
+-- name: DeleteSnakeGame :exec
+DELETE FROM games WHERE id = ? AND game_type = 'snake';
+
+-- name: GetActiveSnakeGames :many
+SELECT * FROM games WHERE game_type = 'snake' AND status < 2;
+
+-- name: CreateSnakePlayer :exec
+INSERT INTO game_players (game_id, user_id, guest_player_id, nickname, color, slot)
+VALUES (?, ?, ?, ?, ?, ?);
+
+-- name: GetSnakePlayers :many
+SELECT * FROM game_players WHERE game_id = ? ORDER BY slot;
+
+-- name: GetUserActiveSnakeGames :many
+SELECT
+    g.id,
+    g.status,
+    g.grid_width,
+    g.grid_height,
+    g.updated_at
+FROM games g
+JOIN game_players gp_user ON g.id = gp_user.game_id AND gp_user.user_id = ?
+WHERE g.game_type = 'snake' AND g.status < 3
+ORDER BY g.updated_at DESC;