Here in Belgium we have cryptographically signed tokens on our legally mandated IDs.

You can use that token to do all sorts of things (my company uses them as authorship signatures for our quality system for medical devices), but if we had some standard like that, then we could have some software that would have a OTP based on that that is a huge list of valid OTPs in a website API or so, not linked to the token itself. (So you would have to trust this software that generates the OTP). You will get people using the same OTP, but that wouldn't matter because it would just be a validity check. Lind of like the old product key generators for games.

Sure this could be abused or gotten around by a programmer or hack, but for 95% of the population it would be effective age verification without giving away any information or statistics. Sure, people could also abuse it and save a code and use it constantly, but then they would already have been verified. Sharing a code around would also happen with teens, but it would be far more effective than not, especially for the low stakes of age verification.