Liability is a complicated matter. Congress waived liability for the pharmaceuticals. If the FDA grants approval, I don't believe anyone assumes liability for adverse effects of the vax.

However, if the FDA approves the vax, then liability could be assumed by employers, but not in the manner you're thinking. Employers would likely be liable for having employees who are not vax "infecting" other people, never mind that the vaxed can also infect others. We live in clown world.

Noone is going to be liable for the vax injuring you. The Biden administration is considering changes in the way it reimbursed hospitals for treatment of the unvax. What that means, they didn't elaborate, but I would guess it means they won't. If the government won't reimburse that also means insurance companies will have standing to also not cover injuries from covid if the person is unvaxed, my guess.