>Question: are private businesses liable for any injury or death from mandating the vaccine
>Answer: Yes private corporation are legally liable for injury or death of an employee if the enforced the vaccine mandate
Where are you getting this info? When I check OSHA site, not seeing that. In fact, they specifically state they don't want to appear to discourage vaccines, so any vax injuries are specifically not recorded on the OSHA record keeping log.
https://www.osha.gov/coronavirus/faqs#vaccine