It's shocking that Apple didn't even touch the Music App in the 10.15.1 update seeing as though some of the biggest issues that users are having with Catalina are related to this app in one way or another. I think part of the problem is that sites (like MacRumors), blogs and YouTuber's aren't giving it enough coverage. If these issues affected the streaming component of Apple Music, it would be top news.
Since I am a heavy iTunes user (with music from a variety or sources - no streaming), I am holding out on upgrading until the Music app is fixed. It's also shocking to hear and read that the Music app feels just as bloated as iTunes did while having less features as well as an awkward and somewhat cumbersome view of your media. This was Apple's chance to make all that was wrong with iTunes right, better, faster, more logical, but none of that happened.
I am going to remain hopeful that Apple will soon invest some much needed time, money and love in the new Music App so users can experience that 'it just works' Apple way, even for those of us who don't stream random music on shuffle, or for those of us who have more than a few hundred songs to manage.