Add a "Send test notification" button to verify push delivery

Adds POST /api/notifications/test, which delivers a canned test push to every
registered device through the existing relay path (not persisted to the
notifications list), wired into the router and OpenAPI. In Settings, a "Send test
notification" button appears under the push toggle, only when push is enabled on
this device, so the full backend -> relay -> FCM -> APNs -> device path can be
verified on demand without waiting for a real device event.

Backend, API and widget tests added; clippy and dart analyze clean.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

frontend/lib/utils/api/oott_api_notifications.dart

@@ -14,6 +14,12 @@ extension NotificationApi on BackendAPI {
     await _dio.post('/notifications/mark_all_as_old');
   }
 
+  /// Asks the backend to deliver a one-off test push to every registered device,
+  /// used from Settings to verify end-to-end push delivery.
+  Future<void> sendTestNotification() async {
+    await _dio.post('/notifications/test');
+  }
+
   Future<({List<Notification> items, int totalCount})> listNotifications(
     bool? isNew, {
     int page = 0,