When you amend your 2020 return you will walk through the federal questions and then will be asked if you want to amend the state.  There is no way to just jump to amending the state without going through the federal interview.
Starting in 2020, Californians who don't have health insurance and who don't qualify for an exemption are subject to pay an Individual Shared Responsibility penalty, or ISR. Form FTB 3853 will be used to claim an exemption or calculate the penalty amount.