How to Search Your Music Library in Catalina
When I tested this, typing any search into the Search field in the upper-left corner of the Music app produced results that I could switch by clicking one of three buttons in a lozenge in the upper-right corner: Apple Music, Your Library, and iTunes Store.
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However, after searching, clicking on an album, and clicking play, which brings up a new playback bar at the top of Music, the buttons were obscured. I had to click the < (back) button at the upper-left corner of the screen a few times, and then the lozenge reappeared.
Previously:
I'm a voice-over (screen reader) user and I ended up creayting a smart playlist specifically for searching as the search offered in the music app wasn't behaving well with voice-over. It's cumbersome at first, but have grown accustomed to using the list, I can find specific items in a 3tb-sized library faster than with the app's search function. But I still have to use the app search for the store as I've not figured out a "smart" (haha!) way to access the store.