feat: Integrate sync status indicators in app title bar and home screen

lib/screens/home_screen.dart

@@ -10,6 +10,7 @@ import 'package:notas/screens/note_editor_screen.dart';
 import 'package:notas/widgets/menu_drawer.dart';
 import 'package:notas/widgets/note_card.dart';
 import 'package:notas/widgets/search_app_bar.dart';
+import 'package:notas/widgets/sync_status_indicator.dart';
 
 class HomeScreen extends StatefulWidget {
   const HomeScreen({
@@ -17,11 +18,15 @@ class HomeScreen extends StatefulWidget {
     required this.repository,
     required this.onOpenSettings,
     this.onVaultInvalid,
+    this.syncStatus = SyncStatus.idle,
+    this.syncErrorMessage,
   });
 
   final NoteRepository repository;
   final VoidCallback onOpenSettings;
   final Future<void> Function()? onVaultInvalid;
+  final SyncStatus syncStatus;
+  final String? syncErrorMessage;
 
   @override
   State<HomeScreen> createState() => _HomeScreenState();
@@ -512,6 +517,10 @@ class _HomeScreenState extends State<HomeScreen> {
                     _isMenuOpen = !_isMenuOpen;
                   });
                 },
+                trailingWidget: SyncStatusIndicator(
+                  status: widget.syncStatus,
+                  errorMessage: widget.syncErrorMessage,
+                ),
                 onSearchChanged: (String query) {
                   setState(() {
                     _searchQuery = query;