Compose only replaces the View part of an Android app, but the In-App Review API doesn't touch Views at all. So you'd just handle all that logic within a click listener as normal, you shouldn't have to do anything different for a Compose app.
From my understanding of it, it's basically just making a service call to Play Services, and the UI that gets shown afterward is a completely separate process. It's just a floating window that displays over your application at that point, not something that gets embedded in your app's UI