Route all database calls through state classes instead of calling
DatabaseManager directly from screen helpers.

- LobbyState: add validateLobby, listenForOpponentReady, startGame,
  listenForGameStart wrapper methods
- SetupState: add confirmSetup, unconfirmSetup, listenForBothSetupReady,
  getOpponentBoard, getFirebaseApi wrapper methods
- LobbyValidator: route through LobbyState instead of DatabaseManager
- LobbyFlowController: route through LobbyState
- SetupFlowController: route through SetupState
- GameNetworkHandler: accept FirebaseAPI via constructor injection
- Thread LobbyState through MainMenuScreen→MainMenuUI→JoinGamePanel
- Thread FirebaseAPI through SetupScreen→GameScreen→GameNetworkHandler

Result: zero DatabaseManager references in screens/ package