jwzlyrics works with Music.app on macOS 10.15. Let me know how it goes.Music.app has a lyric-displaying sidebar now, but I made this work out of curiosity to see how stupid the port from iTunes.app to Music.app was. (Answer: medium stupidity.)
They respond to all the same AppleScript messages, just in a different namespace -- in case doubt lingers about it being a lie that iTunes has been "retired" and Music.app is some brand new thing. No. No, they just renamed the app and deleted a bunch of features. I told you so.
Most of the hassle involved silent failures due to moving target sandboxing API whack-a-mole.
Seems to work for me so far, and you managed not to break Spotify support.
If you ever want to spend more time on jwzlyrics, I have a feature request. Spotify often adds extra text to song titles, which makes the LyricWiki search fail. For instance, Buzzcocks 'Orgasm Addict - 2001 Remastered Version' shows up as 'No lyrics', even though the 'Orgasm Addict' lyrics are in the wiki. If you would strip off the - and following text, lyrics would show up much more often for me.
Easy enough. I already do lots of rewriting/retrying like that. Are these always ASCII hyphens or do you see Unicrud em-dashes and such too?
Of course Spotify doesn't let you copy the song title text from the app, and when I export the playlist using one of the online exporters, it strips the - and following text from the song title. I can search for tracks in the app's search bar, and it finds the exact version (with the -), so I think that is a simple ASCII hyphen.
With version 1.19, it finds the lyrics, but crashes quite often. I have not figured out what triggers the crash.