The government itself—through the CDC—has determined that vaccination status is not of policy importance. There can thus be no compelling interest for the government to forcibly collect this information against the wishes of the population, even were it not stigmatizing. So much more so after the government has spent the last two years publicly demonizing unvaccinated people for their rational and legitimate personal health choices.
https://brownstone.org/articles/us-icd-vaccine-passport-unconstitutionality/
The Impending US ICD Vaccine Passport and Its Unconstitutionality ⋆ Brownstone Institute
The only interest in mandating Covid vaccines, and thus in compiling personal information about vaccination status, is that they reduce transmission. They don’t.
https://brownstone.org/articles/us-icd-vaccine-passport-unconstitutionality/