When I plug my iPod classic into my Mac, the iPod screen says: Do not disconnect. But my Mac doesn't recognize that anything is plugged in.

Hello,

As far as I am aware, the iPod Classic should still be recognised by the latest version of macOS (Monterey) using the Finder.

I do appreciate that some of the steps here are not relevant when troubleshooting a iPod Classic, but can you try the steps you are able to? --> If your computer doesn’t recognise your iPhone, iPad or iPod - Apple Support