refactor(game): 앱 및 게임 세션 개선

- App 초기화 로직 정리
- GamePlayScreen 개선
- GameSessionController 확장

lib/src/features/game/game_session_controller.dart

@@ -225,13 +225,13 @@ class GameSessionController extends ChangeNotifier {
 
   Future<void> loadAndStart({
     String? fileName,
-    bool cheatsEnabled = false,
   }) async {
     _status = GameSessionStatus.loading;
     _error = null;
     notifyListeners();
 
-    final (outcome, loaded) = await saveManager.loadState(fileName: fileName);
+    final (outcome, loaded, savedCheatsEnabled) =
+        await saveManager.loadState(fileName: fileName);
     if (!outcome.success || loaded == null) {
       _status = GameSessionStatus.error;
       _error = outcome.error ?? 'Unknown error';
@@ -239,7 +239,8 @@ class GameSessionController extends ChangeNotifier {
       return;
     }
 
-    await startNew(loaded, cheatsEnabled: cheatsEnabled, isNewGame: false);
+    // 저장된 치트 모드 상태 복원
+    await startNew(loaded, cheatsEnabled: savedCheatsEnabled, isNewGame: false);
   }
 
   Future<void> pause({bool saveOnStop = false}) async {
@@ -382,8 +383,11 @@ class GameSessionController extends ChangeNotifier {
     _state = resurrectedState;
     _status = GameSessionStatus.idle; // 사망 상태 해제
 
-    // 저장
-    await saveManager.saveState(resurrectedState);
+    // 저장 (치트 모드 상태 유지)
+    await saveManager.saveState(
+      resurrectedState,
+      cheatsEnabled: _cheatsEnabled,
+    );
 
     notifyListeners();
   }