Germany has a system in their ID cards that allows anonymous age verification. No one uses it but it’s a technical marvel in my opinion.

The site asks for specific read permissions and the user can decide if he wants to grant them.

One of these permissions is age verification.

You put the phone on the ID card and there is a cryptographic proof that the user connecting to the site is in possession of an ID of a person above 16 (which he of course could have stolen).

So it is technically totally feasible to have good data privacy AND age verification.