I’d like to report you that your app is not showing in the list in Settings -> Notifactions -> (Battle.net) as it should be there to control notifications on iOS on banners, lock screen etc. Even in Settings -> Battle.net, where iOS users can manage more things for the app like using cellular data, language, siri etc. there should be notification section aswell.
Using latest iOS version and version of your app to this current date.
It’s frustrating when you want to receive notifications from your battle.net chat on your phone, you simple dont receive any.