fix(ui): preserve mobile home route and confirm Android exit

ui/flutter/lib/shared/navigation/app_exit_confirmation_controller.dart

@@ -1,3 +1,5 @@
+import 'dart:async';
+
 import 'package:flutter/services.dart';
 import 'package:flutter/widgets.dart';
 
@@ -7,18 +9,37 @@ import '../widgets/app_toast.dart';
 class AppExitConfirmationController {
   static const confirmationWindow = Duration(seconds: 2);
 
-  DateTime? _lastBackAt;
+  OverlayEntry? _toast;
+  Timer? _timer;
 
   Future<void> handleBack(BuildContext context) async {
-    final now = DateTime.now();
-    final lastBackAt = _lastBackAt;
-    if (lastBackAt != null && now.difference(lastBackAt) <= confirmationWindow) {
-      _lastBackAt = null;
+    if (_toast != null) {
+      dispose();
       await SystemNavigator.pop();
       return;
     }
 
-    _lastBackAt = now;
-    showAppToast(context, context.l10n.pressBackAgainToExit);
+    final message = context.l10n.pressBackAgainToExit;
+    final themes = InheritedTheme.capture(from: context, to: Overlay.of(context, rootOverlay: true).context);
+    _toast = OverlayEntry(
+      builder: (_) => IgnorePointer(
+        child: Center(
+          child: Padding(
+            padding: const EdgeInsets.all(24),
+            child: themes.wrap(AppToastContent(message: message)),
+          ),
+        ),
+      ),
+    );
+    Overlay.of(context, rootOverlay: true).insert(_toast!);
+    _timer = Timer(confirmationWindow, dispose);
+  }
+
+  void dispose() {
+    _timer?.cancel();
+    _timer = null;
+    _toast?.remove();
+    _toast?.dispose();
+    _toast = null;
   }
 }