Correct payload in FCM API's. Background handling notifications on iOS and Android.

[designervoid]

I asked a question about the background processing of a cloud message in the Flutter Telegram chat.
One person answered that I only need the correct payload when sending a cURL request (property priority in Android, content_available property in iOS), also that information I found in documenation FireFlutter.
An example of this cURL request:

FCM_KEY=some_value
FCM_TO_KEY=some_value

curl --location --request POST 'https://fcm.googleapis.com/fcm/send' \
--header 'Content-Type: application/json' \
--header 'Authorization: key='"$FCM_KEY"'' \
--data-raw '{
  "to": "'"$FCM_TO_KEY"'",
  "data" : {
      "click_action": "FLUTTER_NOTIFICATION_CLICK",
      "action": "status_change",
  },
  "priority": "high",
  "content_available": true,
}'

But there is another payload as well (link).
Which payload variant is considered correct? Both options work correctly.
However, after fixing the payload, sometimes background messages did not work for me. The notification worked, but the processing did not work inside the FirebaseMessageService, which is initialized in the widget (not in the main function), which is displayed as page.

Additional Information:
I have PushNotificationService class which have properties of fcmToken and methods with listening foreground, onclick notification, background, this methods have parameter RemoteMessage remoteMessage and VoidCallback callback.
Fixed my removing onBackgroundMessage method from PushNotificationService to lib/main.dart:

Future<void> firebaseMessagingBackgroundHandler(RemoteMessage message) async {
  await Firebase.initializeApp();

  debugPrint('🔥 Handling a background message in main: ${message.messageId}');
}

Future main() async {
  WidgetsFlutterBinding.ensureInitialized();
  await Firebase.initializeApp();

  // Android and iOS background handling
  FirebaseMessaging.onBackgroundMessage(firebaseMessagingBackgroundHandler);

  runApp(App());
}