EU is currently on its way to introduce mandatory age verification everywhere.

If I understand them correctly, the proposals are quite different. The US is effectively requiring the implementation of a third party verification service at computer set-up. The EUs approach validates an existing cryptographic identity that says you are over a certain age, without exposing your identification.

Please correct me if I am wrong, this is what I read here.

Do you expect the EU to insist on a different solution once the US solution is in-place in all US-based operating systems?

Yes. They haven't had a problem implementing their own specific regulations before - like alternative app store requirements on iOS or the European editions of Windows.