refactor: update play time property and enhance player settings management

- Changed the play time property from 'play_time' to 'time' in HomeScreen.
- Removed unused player control functions from PlayScreen.
- Added PlayerSettings interface and implemented PlayerSettingsManager for local storage of player settings.
- Refactored PlayRecordManager to merge API records with local player settings.
- Updated authentication logic in authStore to handle optional username parameter in login function.
- Cleaned up and optimized imports across various components.

stores/authStore.ts

@@ -18,6 +18,11 @@ const useAuthStore = create<AuthState>((set) => ({
   hideLoginModal: () => set({ isLoginModalVisible: false }),
   checkLoginStatus: async () => {
     try {
+      const { ok } = await api.login();
+      if (ok) {
+        set({ isLoggedIn: true });
+        return;
+      }
       const cookies = await Cookies.get(api.baseURL);
       const isLoggedIn = cookies && !!cookies.auth;
       set({ isLoggedIn });