Unknown deprecated themes appear in Upgrade Report (Stable and Classy)

This is a confusing warning. The Classy and Stable themes are part of Drupal 9 core and are both located in the web/core/themes directory. So you can't uninstall them like you would with a contrib theme that has been added to your site. You should verify that you're not using another theme that relies on either of those themes as a base theme. As long as they're not being used directly or as a base theme, they should just silently go away when upgrading to Drupal 10.

But, like you reported, I don't know how to satisfy the upgrade status report so that it doesn't complain about these themes even if I'm not using them. So for now I just ignore that warning.

I am not sure if Upgrade Status could detect in a sure-fire way that no other theme is dependent on Classy or Stable. Theoretically that would need to be explicit, but not sure if a fallback system is not in place to fill that in otherwise? I'll ask more frontenders. If there is no fallback system for base themes, then Upgrade Status could check dependencies and verify if the themes are not used and ignore them for the sake of the report.

A quick fix for this is to open the .info files of those themes and set hidden to false. That way they will show up on your appearance tab and you can uninstall them as you would any other theme.

So, go to

1. go to web/core/themes/classy/classy.info.yml
2. on line 9, change hidden:true to hidden:false
3. save the file
4. Go to [site_name]/admin/appearance and uninstall.

Repeat for Stable.