Heres how I got Remote to work with Catalina
I just installed the latest update for Catalina... at first the remote app still didn’t work, but I succeeded in getting full functionality: you need to connect the remote app manually and not with home sharing.
to do this: open remote app => tap settings in upper right corner => add iTunes library => in the music app in your Mac: look for the remote app symbol (arrow with your iPhone name) and enter the 4 digits and you are ready to use the remote app...
I deleted the iTunes Remote from my iPhone, reinstalled it, and then added my Music Library manually, NOT Through Home Sharing, add manually
Went into music, click on my iPhone name, and hey presto, enter the four digit code.
I can now access all 40,000 plus songs on my Mac and control them, via my iPhone