You’re wrong. They did it through OSHA. I know. I was there. My company told us flat out if it became an OSHA mandate we would have to get the shot or resign. Had nothing to do with the States. That was Biden/Feds.
A lot of companies jumped on it immediately with enthusiasm. Others like ours were less eager, dragged their feet, and it ended up getting rescinded before we had to make that decision.