This is a classic case for one time ZKPs. Sure, you can't get around attestation, but the party that needs to verify that you meet age criteria doesn't need to know your age or other private information.

I presume you're concerned by the attesting party's knowledge of both the signature and identify information. Yes, in principle these can be linked, but in practice, it may be difficult or made very difficult, and today, very little of our online activity is really anonymous anyway. It is generally not too difficult to infer identity based on the content someone generates and the bread crumbs they leave behind.

Of course, if the intent is to use age verification as a wedge to monitor everyone, then it will be difficult politically to secure the protections needed to prevent that sort of data fusion.