What you need[0] is a certificate, signed by a recognised provider[1], asserting that email address X is associated with a person aged over 18.
Once you have that, you can then provide it to anyone who asks for it. The certificate provider doesn't need to know who you're proving it to. Literally all they have to do is check whatever information they need to[2] to be happy asserting "Oh yeah, that's an adult".
If your browser (or an add-on for it) wanted to make this easy by storing the certificate for you securely, then that would be awesome, obviously.
But there's no reason why the certification provider needs to know who they're certifying your adulthood to.
[0]Assuming that you want a way to prove you're an adult.
[1]That could be a bank, a government, or anyone else who has sufficient levels of societal trust.
[2]Photo of you, use of a credit card, records of you using that email address for more than 18 years. Whatever makes them happy making that assertion, that they'd be willing to stand up in court and defend their processes if one of their certificates was issued wrongly.