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.
