Flutter FCM data only payload notification is not received when app is terminated

Question

I'm using firebase_messaging: ^11.2.10 and flutter_local_notifications: ^9.4.0 to show notifications. I am sending data only notifications without notification title or body. Most of the time it works, but when the app is terminated and not used for a longer period, notifications won't show until you wake or unlock the phone.

Here is the case: I subscribe to the Firebase background messages.

void main() async {
  WidgetsFlutterBinding.ensureInitialized();
  await Firebase.initializeApp();
  FirebaseMessaging.onBackgroundMessage(MessagingService.subscribeToFCMBackground);
  await NotificationService().init();
  runApp(const MyApp());
  );
}

Inside my MessagingService I get the payload data and there it shows the notification based on the value under the "type" key. Looks like this:

static Future<void> subscribeToFCMBackground(RemoteMessage message) async {
    await Firebase.initializeApp();
    NotificationService().showNotificationByType(_getNotificationTypeFromMessage(message));
  }

static NotificationType _getNotificationTypeFromMessage(final RemoteMessage message) {
    final String notificationType =  message.data['type'] as String;
    return notificationTypeEnumMap[notificationType]!;
  }

Inside the NotificationService I create notification channel, place it inside of NotificationDetails object and pass it to showNotification method. Here is an example of android channel:

final AndroidNotificationDetails _androidNotificationDetails = AndroidNotificationDetails(
      'high_importance_channel',
      'High Importance Channel',
      channelDescription: 'Very important notifications',
      playSound: true,
      sound: RawResourceAndroidNotificationSound(soundFileName),
      priority: Priority.max,
      importance: Importance.max,
    );

...

final NotificationDetails platformChannelSpecifics = NotificationDetails(
      android: _androidNotificationDetails,
      iOS: _iOSNotificationDetails,
    );

...

await flutterLocalNotificationsPlugin.show(
      0,
      'Notification title',
      'Notification body',
      platformChannelSpecifics,
    );

Also I added this to the Android Manifest file:

<meta-data
       android:name="com.google.firebase.messaging.default_notification_channel_id"
       android:value="high_importance_channel" />

Do you guys have any idea how to solve this problem? I would really appreciate any advice or a solution. Thank you!