What version of iTunes dropped synchronization support for iPod Classic?
iPod classic continues to be supported when device syncing was moved from iTunes into the Finder. No device support was removed from iTunes.
If you're having trouble synchronising an iPod with a newer Mac, that sounds like a specific issue that would warrant a specific question.
I can't find the Twitter thread I saw on this topic, but I've found this video that also demonstrates it: https://www.youtube.com/watch?v=fV3itfJyyMM.

An Apple Support article for Big Sur also mentions syncing of iPod classic/nano/shuffle: https://support.apple.com/en-gb/guide/mac-help/mchl923c1147/mac