feat: implement real-time database synchronization with SSE and update backend modules

flutter/lib/features/admin/presentation/admin_database_panel.dart

@@ -1,8 +1,10 @@
 import 'package:flutter/material.dart';
 import 'package:flutter_riverpod/flutter_riverpod.dart';
+import 'dart:async';
 
 import '../../../core/api/api_error_mapper.dart';
 import '../../../core/l10n/l10n.dart';
+import '../../../core/realtime/realtime_sync.dart';
 import 'admin_ai_panel.dart';
 import 'admin_aliases_panel.dart';
 import 'admin_inventory_panel.dart';
@@ -38,6 +40,32 @@ class AdminDatabasePanel extends ConsumerStatefulWidget {
 class _AdminDatabasePanelState extends ConsumerState<AdminDatabasePanel> {
   _DatabaseTab _activeTab = _DatabaseTab.inventory;
   bool _isRefreshingCategories = false;
+  int _panelRefreshVersion = 0;
+  ProviderSubscription<int>? _realtimeTickSubscription;
+  Timer? _realtimeDebounce;
+
+  @override
+  void initState() {
+    super.initState();
+    _realtimeTickSubscription = ref.listenManual<int>(
+      realtimeRefreshTickProvider,
+      (_, __) {
+        if (!mounted) return;
+        _realtimeDebounce?.cancel();
+        _realtimeDebounce = Timer(const Duration(milliseconds: 600), () {
+          if (!mounted) return;
+          setState(() => _panelRefreshVersion++);
+        });
+      },
+    );
+  }
+
+  @override
+  void dispose() {
+    _realtimeDebounce?.cancel();
+    _realtimeTickSubscription?.close();
+    super.dispose();
+  }
 
   List<_DatabaseTabConfig> get _tabConfigs => [
         _DatabaseTabConfig(
@@ -153,7 +181,12 @@ class _AdminDatabasePanelState extends ConsumerState<AdminDatabasePanel> {
         children: [
           header,
           const SizedBox(height: 12),
-          Expanded(child: currentTab.panel),
+          Expanded(
+            child: KeyedSubtree(
+              key: ValueKey('admin-db-${_activeTab.name}-$_panelRefreshVersion'),
+              child: currentTab.panel,
+            ),
+          ),
         ],
       ),
     );