That's probably more an issue with Jellyfin not supporting ratings beyond favoriting something.

I don't really keep bad songs on my server and rotate my "current" playlist sometimes so it's not really how I'd use the app.

For playing on a computer and controlling with your phone? If so, there's KDE Connect that has multimedia controls. That might be what you are looking for?

That would be awesome.

There are groups. Programming a remote wouldn't be too difficult.