If you use something like firebase auth iOS, it is exactly the same premise as in a web app. Your backend stays the same, create a firebase token with the firebase api, and connect exactly the same way as you would in a web app. Done.
Custom Claims would still be done in a firebase function (on create user).
FWI: IMHO, I personally would design an app using Flutter instead of iOS, as it will immediately work on Android and iOS, and it is quick to save mucho dinero.
J