Depends on your country and the law. In the EU AFAIK this would be classified as medical and illegal to query without your consent. And I’ve never heard of anyone who isn’t a doctor getting such a request.
Doctors usually get a ‘required to be vaccinated’ thingy, but else? Never heard of it.
This is exactly what my masters thesis feels like ATM, every attention is on all the AI crap also because the Uni gets grants ont the topic. Everything else just dies