How to get setup with editor styling for the classic editor with Sage 10 + Bud?

Edit: The warning indicates that the URI to the stylesheet is not found, rather a soft-404 HTML page is retrieved.

How is that site hosted? Development, with a VM or container? Production?
When you request the stylesheet URL from within the system where PHP-FPM runs, do you get a stylesheet or rather a soft 404 error page (HTML)?
curl http://domain.test/app/themes/theme/public/tinymce.css?wp-mce-49110-20201110

Have you updated the theme-path in the bud configuration so that it matches the actual path the theme is in (including the theme folder name)?

As a workaround (rather a dirty fix, as core and plugins often rely on a functioning loopback connection and the theme URI should be correct for the assets) you can add the editor styles by relative path than by URI, which does not need a loopback connection: