Guys, it‘s in fact POSSIBLE to play Apple Music (single person-subscription) a Google Chromecast (2.Gen) with IOS(14.4). BUT it has one very major downside: You cannot directly control, what‘s playing. But it seems some kind of influenced by own playlists.
What did I do:
First link your Apple Music-account with the chromecast in Google Home App.
After this in the app main-menu go to media (green button). The should be the app-sign of Apple Music there (in my case, it‘s the only one. At least, choose the device you want to listen to and it should automatically play.
Personally I think the Chromecast itself bypass IOS and streaming directly to Apple Music via Wlan. This is why it‘s possible to control volume and kinds of playing but not the exactly title that is played