Can anyone confirm that the yarnpkg registry is (partly) down?

Yes, probably related to npm problems https://status.npmjs.org/

Some valid registry urls seems to be broken, for example: https://registry.yarnpkg.com/@styled-system/css/-/css-5.1.5....

I've had the same problem for a few hours now. I'm not able to deploy any of my projects.

quick fix would be to use NPM directly

(create a `.yarnrc` file with `registry "https://registry.npmjs.org/"`)

I think this only works if you're doing a clean yearn install. If you have a yarn.lock file already generated, chances are every package is pointing to registry.yarnpkg.com instead.

Ah, yes. Didn't thought about that.