I think one age verification solution that would work while preserving privacy is to sell anonymous cards with an adult verification code on it anywhere where alcohol or adult films etc are sold, as those places can and probably should verify the age of people buying said products anyway so it would not be hard for them.
Then allow people to register their code to an email that then can be checked against by the various adult sites, the email itself can be anonymous on say proton or similar free email services.
To get the code you had to verify your age, but the code itself is not connected to you.
I think that would be a good way of doing it.
The printing of the code cards and such could be done either by the government or a contractor of the government or maybe a certificate authority or domain name service or email providers, who could also in that case run the service to look up email addresses to see if they have been age verified.
Not that anyone here will have any way of helping this idea happen, but I felt like tossing it out here anyway.