feat: add single player snake mode

Add solo mode where players survive as long as possible while tracking
score (food eaten). Single player games start with a shorter 3-second
countdown vs 10 seconds for multiplayer, maintain exactly 1 food item
for classic snake feel, and end when the player dies rather than when
one player remains.

- Add GameMode type (ModeMultiplayer/ModeSinglePlayer) and Score field
- Filter single player games from "Join a Game" lobby list
- Show "Ready?" and "Score: X" UI for single player mode
- Hide invite link for single player games
- Preserve game mode on rematch

db/queries/snake_games.sql

@@ -1,6 +1,6 @@
 -- name: CreateSnakeGame :one
-INSERT INTO games (id, board, current_turn, status, game_type, grid_width, grid_height, max_players)
-VALUES (?, ?, 0, ?, 'snake', ?, ?, 8)
+INSERT INTO games (id, board, current_turn, status, game_type, grid_width, grid_height, max_players, game_mode)
+VALUES (?, ?, 0, ?, 'snake', ?, ?, 8, ?)
 RETURNING *;
 
 -- name: GetSnakeGame :one
@@ -8,14 +8,14 @@ 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
+SET board = ?, status = ?, winner_user_id = ?, rematch_game_id = ?, score = ?, 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;
+SELECT * FROM games WHERE game_type = 'snake' AND status < 2 AND game_mode = 0;
 
 -- name: CreateSnakePlayer :exec
 INSERT INTO game_players (game_id, user_id, guest_player_id, nickname, color, slot)