Add user authentication and game persistence with SQLite

- User registration/login with bcrypt password hashing
- SQLite database with goose migrations and sqlc-generated queries
- Games and players persisted to database, resumable after restart
- Guest play still supported alongside authenticated users
- Auth UI components (login/register forms, auth header, guest banner)

db/queries/games.sql

@@ -0,0 +1,31 @@
+-- name: CreateGame :one
+INSERT INTO games (id, board, current_turn, status)
+VALUES (?, ?, ?, ?)
+RETURNING *;
+
+-- name: GetGame :one
+SELECT * FROM games WHERE id = ?;
+
+-- name: UpdateGame :exec
+UPDATE games
+SET board = ?, current_turn = ?, status = ?, winner_user_id = ?, winning_cells = ?, updated_at = CURRENT_TIMESTAMP
+WHERE id = ?;
+
+-- name: DeleteGame :exec
+DELETE FROM games WHERE id = ?;
+
+-- name: GetActiveGames :many
+SELECT * FROM games WHERE status < 2;
+
+-- name: CreateGamePlayer :exec
+INSERT INTO game_players (game_id, user_id, guest_player_id, nickname, color, slot)
+VALUES (?, ?, ?, ?, ?, ?);
+
+-- name: GetGamePlayers :many
+SELECT * FROM game_players WHERE game_id = ?;
+
+-- name: GetGamesByUserID :many
+SELECT g.* FROM games g
+JOIN game_players gp ON g.id = gp.game_id
+WHERE gp.user_id = ?
+ORDER BY g.updated_at DESC;