I am having the same problem.
I frequently listen to local (French, British) national broadcast radio stations streamed through Apple Music.
Since upgrading to iOS 15, these are still listed as before, and the app changes to display the station as before, and even says "LIVE" with a square stop button - but there is no audio.
The stations can still be listened to via their own apps, their web pages or using the TuneIn Radio app, but not through Music ...
Have posted the same on Apple/Support.