I just upgraded to Catalina 10.15.5. I see my iPod device in my finder. The earlier sync problems I reported are gone.
I can also go into Music (the new iTunes) and the device is listed there too. Though the sync operations are no longer there, it does show me an accurate list of all the songs on the iPod.
Essentially, all the music functionality seems to be there and functioning correctly, only split across Finder and Music as opposed to all being lumped into iTunes.
@SaltMarshGirl, sorry to hear the book interface isn't as good. I presume the Books app doesn't show the device? I'm unable to find a terminal command either: I tried to drag the device to the terminal to get macOS to construct a pathname, but all it did was remove the device from Finder entirely, and I had to spend several minutes to figure out how to get it back in there (-:.
But most of all, as @SaltMarshGirl says — the iPod isn't trash yet! Indeed, I've been desperately hoping to change my playlists and can do so now.