I see two possible solutions to get rid of the not working Music app:
1) do not upgrade to Catalina;
2) continuing to use iTunes under Catalina. However iTunes is artificially disabled by Apple under Catalina (why?), but it can be patched by the "Retroactive" application to run smoothly on Catalina.
A Further advantage is have Radios in iTunes (practically non existing anymore in Music app) and get rid of Books apps which stores audiobook in the same user Container location as Music artworks (big problem if you have several Gb of audiobooks).
I still hope that Apple will change direction, because, at the moment, from my point of view, both Music and Books applications are not usable. Hopefully, users will give some strong feedback to Apple.