Ah, OK. As I read through the rest of the thread I saw Mr. Hakes' method and it eventually worked for me, although I found his directions slightly confusing. I've annotated them below:
Open Music in Catalina.
Open the Remote on your iPhone/iPad.
You should see a blank screen. [He means on the Remote app. I didn't; I saw my music libraries.
Click on Settings in the upper right corner. [Of the Remote app.]
Turn off Home Sharing; turn on Home Sharing and then set up manually the screen changes. (maybe you have click on add an iTunes library) [Again, on the Remote app. On one iDevice I did have to click add a library. On another device it would only let me do this after I deleted the existing library.]
In Music on your Mac, click on the device. [On the left-hand side of the Music window you will see Devices listed. You will only get the opportunity to enter the four digits if the icon has changed from a picture of a device to the "Remote" icon. If you don't have this, go back to your Remote app and try to add a library again.] Enter those 4 numbers. That should do it.
The weird thing is that this procedure turn off Home Sharing on the device.
But it works.
Kind of not Apple in execution but it does work.
The library will be the name of your old iTunes library but that is updated by anything you do in Music. Well it does on mine.
Hope that made sense.