The government already have all your personal information. If you mean that you don't trust a government API to do age verification, then that's already an option in some countries and it doesn't have to expose anything.

Denmark have MitID, which is a sort of government OIDC/OAuth2 thing. There's no issue in having it expose only a single claim, such as age, or adult=true/false in age verification scope. You don't have to open the floodgates to government data, in fact Denmark has navigated that pretty well through the last three iterations of our government issues online ID scheme. There's even laws preventing cross referencing data from different database, in the case that you for some reason have access to it.

Where do you live where the government does not have your basic information - name & date of birth? You're being unreasonably paranoid IMO.