In my post I acknowledged that disability would be an exception. It would also be a violation if the employer only required women or people over 50 to be vaccinated, but that's a civil rights violation.
...what’s the enumerated power that allows the federal government to establish a database of your medical history?
I haven't thought much about it but I'd say tracking vaccination status during a pandemic could be good for the general welfare of the nation.
How would that medical history collection not be a violation of the 4th Amendment?
At least in my state the vaccine consent I agreed to explicitly allows my health care provider to give my vaccine status to the state and the state to share it with the federal government.
The 4th doesn't apply to information freely offered by the individual and no government in the US is mandating the vaccine as far as I know.
Forcing one to surrender their privacy in order to get a vaccine is a form of extortion.
I don't think you get it. Not having the vaccine would very likely be the disability itself. Since it's a disability, you can't discriminate against those people. A law professor writes about the legal hurdles to these possible vaccine 'passports' below.