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.
So you should assume the government can track you, because you should assume both will be streaming those identifiers to it.