California conforms to the federal entity classification election. You don’t have to file anything separately with the state of California for the S election to be allowed in California. You should file a 2022 Q1 Form 100-ES and pay at least the $800 minimum tax by April 15, 2022 (more if your income is high enough).
The exception that allows new corporations to not pay the $800 minimum tax does not apply where you were already in business and simply made an election to be taxed as a corporation.
Do not pay the $800 tax as an LLC tax in 2022.
After you file your first 100S with the state of California, the FTB will issue you a corporation number to use on future filings.