In China, the vaccine testing data is already integrated into their social credit score system, so you can't get on public transit, etc. without completing the vaccine milestones.

In the US, the govt. has an internal system called XKeyScore that tracks your email, web and credit history.

In Australia, they have a "private" vaccine tracking app, but from Day One the police admitted having access to the database. (The police called reporters stupid for believing the app data was ever private.)