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?


Super easy. Technology has existed for quite some time and was already used in the encrpytion of web traffic.
Basically: you sign up with your “age verification institution” (ideally a service of your government because they have your ID anyway and no profit motive). This involves createing a private key (reaaaaaaaaaaly long password that is saved in a file on your device) and saving the public key with that institution. They also check your ID to ensure your identity and your age.
When you want to visit a 18+ website, the website sends you a nonce (loooooong random number). You take that nonce and send it to the verifier, along with a signature of your private key (and the age they want you verified against). The verifier verifies your signature using your public key. They then sign the nonce with their own private key, thereby verifying, that you, the owner of your private key (whos identity and age they have verified) are above the asked age theshould. You then send the signed nonce back to the 18+ website and they can verifiy the signature to confirm that a trusted age verifier has verified your age.
The site never has access to your identity and the verifier never knows which site you visited, only that you wanted to visit a website that wants to know if you are of a certain age.
(The corresponding technology was used for OCSP Stapling in TLS verification … and has been discontinued last year because nobody was using it …)