DH actually works pretty closely with quite a few US universities, and we have several friends who work for them too. It looks like some (mostly northern) will absolutely insist everyone is vaccinated, while others (mostly southern) will claim that they have no legal authority to require vaccination, and just not bother.
As a result Covid will not be going away anytime soon, but as long as staff/students have been offered it then there is absolutely no reason they can't go back to fully in-person next semester.
Given how much university costs here, I think people will start suing universities soon if they're not back in-person.