You mean other than the health insurance they (hopefully!) provide you, right?
Even beyond that, the idea that the piece of cardboard that the CDC gave you constitutes meaningful (much less private) medical data about you is facile. Depending on the state you live in, your employer de facto has knowledge of your medical history: if you went to a public or private school in most US states, they were legally required to obtain proof of your vaccination against multiple diseases. The reason your job doesn't ask for that proof independently is because we've succeeded at lower levels in mandating it.
> also, i'm 100% wfh since before the pandemic started. I'm endangering no one at my workplace.
That's fine. But your workplace (presumably) isn't your only social sphere.
Edit: You're also (again, presumably) going to return to your workplace or travel on behalf of your employer at some point.
I got vaccinated to protect myself and those around me. My job has no business in my health records. period.
edit: also, i'm 100% wfh since before the pandemic started. I'm endangering no one at my workplace.