Prove it. You are spreading a falsehood. There was a law passed in I think 1985 that no vaccine manufacturer can ever be sued. If someone has a problem with a vaccine, they go to some government agency, and try to scrounge for something.
Fraud and some other things can make them lose that exemption but yes vaccine injuries do go through the FedGov.
You are wrong. If there is fraud (fake tests and results) or the vaccine is defective (improperly manufactured, impure, incorrect contents, etc.) they can be sued. Under emergency use they cannot be sued but when approved they can then be sued for the above instances which abound in the current EUA vaccines.