Businesses that require vaccines under EUA are taking a legal risk, but, given the circumstances, also have good legal arguments for the mandates. And whether it is appropriate or not is very fact dependent. I do not expect many businesses to require a vaccine in these conditions; but claiming they cannot legally do so is inaccurate, and can increase harms.
First one I found. DuckDuckGo is your fren. https://blog.petrieflom.law.harvard.edu/2021/02/24/employer-mandate-covid-vaccine-eua/
That source seems to say the opposite.
I only skimmed it. There are many sources I would surmise. You can look for yourself for this substantiation.
https://www.statnews.com/2021/02/23/federal-law-prohibits-employers-and-others-from-requiring-vaccination-with-a-covid-19-vaccine-distributed-under-an-eua/