To be clear, I’m not advocating for online age verification. I’m very much against it in any form. I’m just curious from a technical standpoint if it’s possible somehow to construct an accurate age verification system that doesn’t compromise a user’s privacy? i.e., it doesn’t expose the person’s identity to anyone nor leaves behind a paper trail that can be traced to that person?


Technically this works EXCEPT the required third party. Either it’s the government and you have to trust them with information of knowing everything that required age verification or its separate company that can and would sell your data to data brokers. Being free and NOT the government seems mutually exclusive.
The verifier does not have the information which sites you use. That’s the point of the setup. All communication goes through you, never the site to the verifier directly. You only pass cryptographic values between them that does not include identifiable information (neither about you to the website, nor about the website to the verifier). The verifier knows who you are, the website knows that you are old enough. Nothing else.
Oh I missed that separation before. Ok my bad.