GrapheneOS has pretty much perfect app compatibility. I don't think I've ever ran into an issue in around a year of using it as my daily driver.

Most apps function without Play Services, but you may lose some functionality like notifications, and a couple apps do very rarely genuinely break. But, that's where Sandboxed Play Services comes in, which you can even put in an entirely separate user profile if you want to, so that you can still safely use those apps.

But yeah, I've personally had no issues with app compatibility. Even my bank app works perfectly on Graphene (didn't even require Play Services either!).