Agree, different statutes in different states. In California, where I practiced in a legal-adjacent field, there were some damage caps in medical malpractice, certain vehicular cases and probably some others, but here's what a legal site says generally:
"If you're unable to negotiate a suitable settlement outside of court, filing a lawsuit may be your best option. If you go to court, the money award you receive isn't limited by the insurance policy limits. California's personal injury damages laws set how much you can receive from the at-fault party or parties."
Naturally, it depends on what the judge or jury awards you.