Implement shared_preferences persistence layer

Use a constant prefix map or a static const List of all managed keys to ensure clearAll() is exhaustive — avoid relying on prefix scanning as shared_preferences does not natively support key prefix listing. Instead, maintain the set of known keys as a class-level constant. Inject SharedPreferences through the constructor and register the repository as a singleton in the dependency injection layer (Riverpod provider or BLoC service locator) so the same instance is shared across the app. For lifecycle event integration, subscribe to Supabase.instance.auth.onAuthStateChange inside an init() method and call clearAll() on AuthChangeEvent.signedOut and on role change events — dispose the subscription in a dispose() method.

Serialize snapshots with jsonEncode(snapshot.toJson()) and deserialize with NavigationStackSnapshot.fromJson(jsonDecode(stored)) wrapped in try/catch to handle corrupted data gracefully (return null on parse error).

Unit tests in task-003 cover all persistence methods using SharedPreferences.setMockInitialValues(). This task should include integration smoke tests that run against a real SharedPreferences instance on a test device (or via integration_test package) to verify actual disk persistence across app restart simulation. Specifically test: save tab index → restart simulation → load tab index returns the saved value. Cover all 5 tab indices.

Test clearAll() by saving data for all tabs then calling clearAll() and asserting every loadX() returns null.