Without being able to access the iTunes Music Library.xml file, 3rd party products such as Bose Soundtouch can't locate the library. How is this resolved?

Use File > Library > Export Library... to create an XML file representing the library. Rename it if required to match Bose's expectations.

tt2

In my case, the Bose Soundtouch continued to work after the elimination of iTunes, but would not sync with additions/changes to the music files in Catalina. Not being very savvy with naming/moving files on the Mac, I opted to (1) remove the music library in the Soundtouch app, (2) download iTunes via retroactive, (3) drag and drop copies of my music and playlists in the Mac music file to the empty files in ITunes and (4) use the Soundtouch app to add the library back via iTunes. So far it works fine without going through Apple Music, but I know any future changes to the files in Music will need to be manually repeated in the iTunes file for the Bose app to pick it up.