This is normal for interacting with small children without being directly supervised by a licensed professional. You'll also need to get a TB test and, depending on how much time you're spending with the kids, may need to take some anti-sex-abuse training. AB506 is the relevant bill; you can read it at https://leginfo.legislature.ca.gov/faces/billNavClient.xhtml... .
Having gone through this myself recently, it should not apply to parents attending events, if they are just a passive attendee, such as being in an audience for a school play. It does apply to any administrator, employee, or regular volunteer. Iirc the regular volunteer part has a number of hours of total volunteerism over the course of a year that is relatively low so if you are helping out with any frequency then yes, this probably applies.
Apparently the LA school system has been doing this since 2018 for volunteers. What do you mean by "participate"? Volunteer, or attend?
Your kid goes to a CA school, sure, but it's not a "California" school, it's a Sacramento school district or San Diego or LA or other locality's school district. Many other school districts don't have this requirement, or didn't when LA instituted theirs.
