I have been experiencing the same exact problem for over a month now. Can’t play Apple Music on WiFi or Data I keep getting the error message “ Network connection lost” and it skips through all the tracks even if they have been downloaded.
I have been chatting with Apple and their engineerings for days but still no fix for the problem which is super annoying because I have been paying despite not been aple to use the App.
They have told be to Go on settings-> general -> transfer or reset iphone -> press on reset and in the last popup you press on reset network but for me didn't work.
Then they told me to turn off wifi and data -> turn the airplain mode on -> go on the Apple music app for 30 secs -> turn on the data again, it didn't work either.