As I said, I don't have Music, nor Catalina.
However, does the "iCloud" System Pref have "Music" in the list of apps that use iCloud? If it does, are there any "Options" for it? And, make sure it (Music) is enabled, of course. Lastly, make sure your iPhone is directly connected to the Mac, not through a charging port of an external USB hub.
That's it, I have no more suggestions and cannot use apps/OSs that I don't have. Sorry.
Only other option I can think of is to re-install Music, probably from your Recovery Drive.