I don’t know if this would work on iOS (or if it’s already implemented), but any idea if I can make the app pop up directly every time I unlock the phone? This would mean that I don’t need open the app manually myself /keep the app on top before I lock the screen.
It's not possible to overlay apps after unlocking on iOS.
But I found a way how to change UX to fulfil that. All intentions should be marked as failed or successful after finishing, so the user should back to the app before phone lock. So by locking your phone in the app, you will not forget about filling intention next time.
That's the only allowed way I found for iOS. There is a way how to show your app immediately after unlock, but it requires using private API that is not allowed by the App Store.