I've been using Catalina for some time with no real problems. I did finally see where the search bar in Music was located. So I type in the information and select something I want to check out.
I'm taken to that particular album and all the tracks are there. But click on a track, which in the past would have given me the option to listen to a sample or purchase. Now another window opens asking if I want to join Apple Music. When I select the "Not Now" option the window disappears and I'm left with no option to purchase the selected song. For some reason I can't get the screenshot to load. It's only 307 KB.
I mainly use the music on my iPhone in a vehicle anyway, and iTunes Store on the phone works as it always has. I can search a song, select it and buy it without Apple Music being involved in any way. I have no interest in a monthly subscription.
Edit: Apparently some things can be easily purchased because a screen that shows an option similar to the "old" way appears, but only for some music. Other selections only show the Apple Music option that I mentioned. Oh well.