Phase 3.1 WS2: FCM fallback Flutter + CC, unread badges, dynamic ping

- Control center: add mitra ping config UI (require ping toggle + interval)
- Mitra app StatusNotifier: honor require_ping and ping_interval_seconds
  from API; skip heartbeat when ping not required
- Both apps: update notification services for FCM deep-linking
  - mitra_app: handle chat_request (open_accept), session_closing
  - client_app: handle session_closing, paired
- Unread badge providers:
  - mitra_app: UnreadSessions provider (polls active-with-unread, badge
    on active sessions button)
  - client_app: UnreadCount provider (polls active-with-unread, badge
    on _ActiveSessionCard)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

mitra_app/lib/features/home/home_screen.dart

@@ -4,6 +4,7 @@ import 'package:go_router/go_router.dart';
 import '../../core/auth/auth_notifier.dart';
 import '../../core/status/status_notifier.dart';
 import '../../core/chat/chat_request_notifier.dart';
+import '../../core/chat/unread_notifier.dart';
 import '../chat/widgets/incoming_request_sheet.dart';
 
 class HomeScreen extends ConsumerStatefulWidget {
@@ -159,16 +160,23 @@ class _StatusToggle extends ConsumerWidget {
   }
 }
 
-class _ActiveSessionsButton extends StatelessWidget {
+class _ActiveSessionsButton extends ConsumerWidget {
   const _ActiveSessionsButton();
 
   @override
-  Widget build(BuildContext context) {
+  Widget build(BuildContext context, WidgetRef ref) {
+    final unreadCounts = ref.watch(unreadSessionsProvider);
+    final totalUnread = unreadCounts.values.fold(0, (a, b) => a + b);
+
     return Column(
       children: [
         Card(
           child: ListTile(
-            leading: const Icon(Icons.chat_bubble_outline),
+            leading: Badge(
+              isLabelVisible: totalUnread > 0,
+              label: Text('$totalUnread'),
+              child: const Icon(Icons.chat_bubble_outline),
+            ),
             title: const Text('Sesi Aktif'),
             trailing: const Icon(Icons.chevron_right),
             onTap: () => context.push('/sessions'),