feat: Implement _LoggedInView UI and AuthState improvements

Implements the UI for the _LoggedInView in home_screen.dart, including:
- An AppBar with a Profile icon that navigates to the profile screen.
- A ListView.builder displaying example items.
- A FloatingActionButton.extended for Logout that calls the `authState.logout()` method.
- Adds a `logout()` method to `AuthState` to clear the login state.
- Modifies the `toggleLogin()` method in `AuthState` to accept an optional boolean value for explicit state control.
- Ensured code formatting and resolved any linting issues.

lib/auth/auth_state.dart

@@ -4,8 +4,13 @@ class AuthState extends ChangeNotifier {
   bool _isLoggedIn = false;
   bool get isLoggedIn => _isLoggedIn;
 
-  void toggleLogin() {
-    _isLoggedIn = !_isLoggedIn;
+  void toggleLogin({bool? value}) {
+    _isLoggedIn = value ?? !_isLoggedIn;
+    notifyListeners();
+  }
+
+  void logout() {
+    _isLoggedIn = false;
     notifyListeners();
   }
 }