- Integrate `useRouter` in `UserProfile.vue` and `useAuth.ts` to manage navigation after logout.
- Update `handleLogout` in `Navbar.vue` to reflect that redirection is now handled within the `auth.logout()` function.
- Replace identity management with a new authentication system across the application.
- Update App.vue to integrate LoginDialog and remove PasswordDialog.
- Modify Navbar.vue to handle user authentication state and logout functionality.
- Enhance Home.vue to display user information upon login.
- Implement routing changes in index.ts to enforce authentication requirements for protected routes.
