Byku Will my government know things like when I verify my age to buy alcohol?
Specifically, it depends on the requirements of your government.
Generally speaking, even without the Double-Blind system(still under development) the website should only know if your are of legal age while the government(or whatever identify certification authority you use) should only know that one website asked for your age.
For online purchases it's better than physical ID because the website will only have your age and thus will be unable to sell\lose your personal info. Physical ID would require you to send them a copy\scan of it, which will obviously contain much more information and become a identity theft risk.
It's also worse than a physical ID because the government would be able to know you attempted(not necessarily completed) a purchase of age-restricted products on a certain website.
This could be mitigated by the website implementing an account system where they only ask your age once and then not anymore for future purchases(it's not like you are going to get younger), but this also depends on government regulations.
When\if the double-blind system will be implemented, the government will instead only know you certified the App and will have no way to know when the app gets used to give your age(or other information).