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();
   }
 }

lib/home/home_screen.dart

@@ -26,7 +26,42 @@ class _LoggedInView extends StatelessWidget {
 
   @override
   Widget build(BuildContext context) {
-    return const Center(child: Text('Logged In'));
+    final authState = Provider.of<AuthState>(context, listen: false);
+
+    return Scaffold(
+      appBar: AppBar(
+        title: const Text('Welcome Back!'),
+        actions: [
+          IconButton(
+            icon: const Icon(Icons.person),
+            onPressed: () {
+              context.go('/profile'); // Navigate to profile screen
+            },
+          ),
+        ],
+      ),
+      body: ListView.builder(
+        itemCount: 20, // Example items
+        itemBuilder: (context, index) {
+          return Card(
+            margin: const EdgeInsets.all(8.0),
+            child: ListTile(
+              leading: const Icon(Icons.star),
+              title: Text('Item ${index + 1}'),
+              subtitle: const Text('This is an example item.'),
+            ),
+          );
+        },
+      ),
+      floatingActionButton: FloatingActionButton.extended(
+        onPressed: () {
+          authState.logout(); // Call logout method
+        },
+        label: const Text('Logout'),
+        icon: const Icon(Icons.logout),
+      ),
+      floatingActionButtonLocation: FloatingActionButtonLocation.centerFloat,
+    );
   }
 }