Route Android system back through the Flutter shell

Constraint: SRS-163 requires Android back to be handled by the shell/platform layer, and the Dart service existed but was not wired into the live app.
Rejected: Leave BackIntentService test-only and unwired | System back would bypass app policy on Android.
Confidence: medium
Scope-risk: narrow
Directive: Keep back-intent probe state in sync with every new dialog or pushed route added to the Flutter shell.
Tested: dart format apps/chanora_flutter/lib/main.dart; flutter analyze lib/main.dart test/services/back_intent_service_test.dart; flutter test test/services/back_intent_service_test.dart
Not-tested: Manual Android device back-navigation smoke test

apps/chanora_flutter/lib/main.dart

@@ -20,6 +20,7 @@ import 'l10n/generated/app_localizations.dart';
 import 'services/android_permissions_service.dart';
 import 'services/app_bootstrap.dart';
 import 'services/audio_lifecycle_service.dart';
+import 'services/back_intent_service.dart';
 import 'services/channel_join_error_mapper.dart';
 import 'services/connection_phase_state.dart';
 import 'services/ios_permissions_service.dart';
@@ -93,6 +94,9 @@ Future<void> _finishDeferredStartup() async {
 class ChanoraApp extends StatelessWidget {
   const ChanoraApp({super.key});
 
+  static final GlobalKey<NavigatorState> navigatorKey =
+      GlobalKey<NavigatorState>();
+
   @override
   Widget build(BuildContext context) {
     return AnnotatedRegion<SystemUiOverlayStyle>(
@@ -114,6 +118,7 @@ class ChanoraApp extends StatelessWidget {
           colorSchemeSeed: const Color(0xFF3F51B5),
           scaffoldBackgroundColor: _appSurfaceColor,
         ),
+        navigatorKey: navigatorKey,
         localizationsDelegates: AppL10n.localizationsDelegates,
         supportedLocales: AppL10n.supportedLocales,
         home: const _BetaHome(),
@@ -220,12 +225,24 @@ class _BetaHomeState extends State<_BetaHome> with WidgetsBindingObserver {
       AndroidPermissionsService();
   final IosPermissionsService _iosPermissions = IosPermissionsService();
   final UiPreferencesService _uiPreferences = const UiPreferencesService();
+  late final BackIntentService _backIntentService;
+  int _modalRouteDepth = 0;
 
   @override
   void initState() {
     super.initState();
     WidgetsBinding.instance.addObserver(this);
     HardwareKeyboard.instance.addHandler(_handleFocusedPttKey);
+    _backIntentService = !kIsWeb && Platform.isAndroid
+        ? BackIntentService(
+            pttActiveProbe: () => _audioStats?.pttActive ?? false,
+            modalOpenProbe: () => _modalRouteDepth > 0,
+            atRootProbe: () => !_chatOpen,
+            closeTopModal: _closeTopModalRoute,
+            popRoute: _popTopRoute,
+          )
+        : BackIntentService.noOp();
+    _backIntentService.start();
     _eventsSub = rust.eventsStream().listen(_onEvent);
     // SDD-106 §5: subscribe to Kotlin -> Dart permissionStateChanged
     // events as early as possible so the listen-only banner reflects
@@ -246,6 +263,38 @@ class _BetaHomeState extends State<_BetaHome> with WidgetsBindingObserver {
     unawaited(_loadUiSettings());
   }
 
+  Future<T?> _showTrackedDialog<T>({
+    required WidgetBuilder builder,
+    bool barrierDismissible = true,
+  }) async {
+    _modalRouteDepth += 1;
+    try {
+      return await showDialog<T>(
+        context: context,
+        barrierDismissible: barrierDismissible,
+        builder: builder,
+      );
+    } finally {
+      if (_modalRouteDepth > 0) {
+        _modalRouteDepth -= 1;
+      }
+    }
+  }
+
+  void _closeTopModalRoute() {
+    final navigator = ChanoraApp.navigatorKey.currentState;
+    if (navigator == null || _modalRouteDepth == 0 || !navigator.canPop()) {
+      return;
+    }
+    navigator.pop();
+  }
+
+  void _popTopRoute() {
+    final navigator = ChanoraApp.navigatorKey.currentState;
+    if (navigator == null) return;
+    unawaited(navigator.maybePop());
+  }
+
   Future<void> _loadUiSettings() async {
     try {
       final settings = await _uiPreferences.loadSettings();
@@ -270,8 +319,7 @@ class _BetaHomeState extends State<_BetaHome> with WidgetsBindingObserver {
         final permsExplained = await _uiPreferences.hasExplainedPermissions();
         if (!permsExplained) {
           if (!mounted) return;
-          await showDialog(
+          await _showTrackedDialog(
-            context: context,
             builder: (ctx) => AlertDialog(
               title: const Text('Permissions'),
               content: const Text(
@@ -675,6 +723,7 @@ class _BetaHomeState extends State<_BetaHome> with WidgetsBindingObserver {
   void dispose() {
     WidgetsBinding.instance.removeObserver(this);
     HardwareKeyboard.instance.removeHandler(_handleFocusedPttKey);
+    _backIntentService.stop();
     _eventsSub?.cancel();
     _statsTimer?.cancel();
     _snapshotRefreshInFlight = false;
@@ -754,8 +803,8 @@ class _BetaHomeState extends State<_BetaHome> with WidgetsBindingObserver {
   void _showPermissionDeniedDialog(String rawError) {
     final l10n = AppL10n.of(context);
     final isNetwork = rawError.contains('9987') || rawError.contains('connect');
-    showDialog(
+    unawaited(
-      context: context,
+      _showTrackedDialog<void>(
         builder: (ctx) => AlertDialog(
           title: Text(
             isNetwork ? l10n.networkPermissionTitle : l10n.permissionDenied,
@@ -792,6 +841,7 @@ class _BetaHomeState extends State<_BetaHome> with WidgetsBindingObserver {
             ),
           ],
         ),
+      ),
     );
   }
 
@@ -1168,8 +1218,7 @@ class _BetaHomeState extends State<_BetaHome> with WidgetsBindingObserver {
 
   Future<void> _onConfirmDisconnect() async {
     final l10n = AppL10n.of(context);
-    final confirmed = await showDialog<bool>(
+    final confirmed = await _showTrackedDialog<bool>(
-      context: context,
       builder: (ctx) => AlertDialog(
         title: Text(l10n.disconnectConfirmTitle),
         content: Text(l10n.disconnectConfirmBody),