Our county and state in California both have systems in place. It is nice as we have or physical cards but also digital records of our status. I am glad to have it in my phone in a verifiable way and not have to carry that flimsy notecard everywhere.Those databases might already exist on the state level. We have one of those win a million bucks by getting vaccinated contests. In the sign up process we had to agree to allow them to verify our vaccination status but it never asked where or by whom we received the vaccine.
Not sure how they would do that without some kind of database.