With ZKP age verification, services will not be able to track you without help from the CA. The CA will not be able to track you without help from the services. Both will contain the necessary information in their databases that when combined deanonymize you. The CA is the central authority/certificate authority.
So you should assume the government can track you, because you should assume both will be streaming those identifiers to it.
That's not really possible to explain in this space, unfortunately, but the overall idea is that there are mathematical techniques that allow you to prove that you have a valid certificate without revealing which one it is.
That would be ideal. However, this is tech proposal which takes so much of the slop out of the entire thing. With this implementation, there is no profit in it, unless your government is directly cooperating, aka a scandal in many countries.