These are the two articles I recalled reading on this subject.
The first one shows that no vaccine maker of an approved vaccine can be sued. Doesn't matter if it's the newly developed Covid vaccine or the 40 year old Measles vaccine.
According to 42 U.S. Code § 300aa–22, "No vaccine manufacturer shall be liable in a civil action for damages arising from a vaccine-related injury or death associated with the administration of a vaccine after October 1, 1988, if the injury or death resulted from side effects that were unavoidable even though the vaccine was properly prepared and was accompanied by proper directions and warnings."
The first one shows that no vaccine maker of an approved vaccine can be sued. Doesn't matter if it's the newly developed Covid vaccine or the 40 year old Measles vaccine.