At all travel points trains/planes the government will require a vaccine passport check. This check will require the person to provide id to match against the vaccine passport information. At this point your information/location are verified and entered into a government system.

As for tracking by private companies. At your local pizza shop your location may not be tracked through the open source clients you list but at larger venues the opportunity for information gathering/sharing is possible. Previously one could buy a ticket to a game from someone outside now everyone eventing must identify themselves.