A different approach using said TuneIn feature:
In the Music.app Radio section, look up all of your favored stations and paste the urls in a
Dictionary
in Shortcuts.app.
With Monterey and newer you can do this directly on the Mac.
On your iPhone create a Home Screen icon for that shortcut for easy access.
Unfortunately this TuneIn method includes their annoying added jingle plus ads and probably lacks some specific radio stations.
Of course you could insert the official .m3u streams but then the selected radio station / stream would play in a Safari tab instead of Music.app.
edit: Ok, I forgot, on iOS the Shortcuts.app is not installed by default and you didn't want an additional one...