Supervised devices do not require an Apple ID, but you can still use one.

All my iPhones have been supervised and I continue to use a number of apps and services linked to my Apple ID.  No worries, all the standard functionality remains even if the device is supervised...unless someone blacklist the apps.

To supervise or not, here is a comparison:

https://docs.vmware.com/en/VMware-Workspace-ONE-UEM/services/iOS_Platform/GUID-iOSFunctionalityMatri...

Additional info:

https://docs.vmware.com/en/VMware-Workspace-ONE-UEM/2011/UEM_Managing_Devices/GUID-AWT-ENROLLMENT-SU...

I will say from experience, it is a bit more work from an administrative standpoint to enable device supervision, however to me its worth in when you need to enable or clear an activation lock from a terminated employee.

Using Apple Music on a supervised business iOS device can be a bit tricky. Typically, supervised devices limit the use of personal Apple IDs, which is essential for Apple Music access. While it might be challenging to get Apple Music up and running on such devices, you could explore alternatives like Spotify. If you're torn between the two, I recommend checking out a detailed comparison between Spotify and Apple Music to find the best fit for your needs. Download or visit this link for an in-depth analysis: https://www.spotifyguru.com/spotify-vs-apple-music/. Good luck!