How do I download music to an iPod classic after restoring it?

Which iPod Classic do you have? The last one was produced in 2009 and was available until about 2014. I have what was originally called iPod Photo from 2004 but was retro-named Classic when the name was added to the range.

Either way, it's unlikely you will be able to move your music across to your iPod if you are using Sequoia on your Mac. At some point in the past these obsolete iPods lost touch with macOS and I have not been able to sync my audio with any recent macOS for a few years now. Instead, I have maintained an old Mac Mini with 10.13 High Sierra specifically for this purpose because syncing wasn't possible with my current Mac. The Mini is small and unobtrusive and I can connect to it from my iMac with Screen Sharing so it's a system which is working well for me at the moment.

This conversation has more to say on why the old iPods have been left behind.

The future pathway for my audio listening is to use a retired iPhone 12 (which has the current version of iOS by the way) as my iPod replacement and perhaps acquire some AirPods. I listen to audio at home so I don't need and don't like to use my current iPhone for audio. But for now, my 20+ year old iPod is powering along in partnership with my not much younger Mac Mini. On the plus side you have to acknowledge that Apple hardware lasts for ages.