After upgrading to Catalina, is there a way to remote control the Apple Music app on my desktop? I have upgraded to Catalina and I have enabled Home Sharing.  

I am able to connect to an airplay speaker from my desktop and from my phone.

I also have a set of non-wifi enabled speakers attached to the desktop.

From my phone, I am able to access the music library on my desktop, but I am unable to remote control the Apple Music app running on my desktop from my phone.  Is this possible?
No - not today. Apple needs to update their iTunes remote so it works with the Music app in catalina.