CSS is never going to be able to, on its own, read and exfiltrate the data necessary.

CSS knows a lot, and it can send it back via image requests, triggered in states through animations, 'lazier'-loading, unqie font-choosing, etc.

https://blog.sheddow.xyz/css-timing-attack/

  You're relying on things like access logs at that point.

Well, yes. The timing and unique request path make identifying possible. And CSS can be dropped in context by other users, crafted to refer to a different domain, so CSS worms can definitely ex-filtrate data without the webmaster being evil.