My understanding is that SF's rule will include all indoor public spaces (e.g., restaurants, gyms, bars, indoor concerts, etc.). I assume there won't be an exception for children under 12 to keep them safe but I'm uncertain.
We are probably one of the more conservative families out there when it comes to COVID, though. We only ordered takeout and kept the kids at home until they were vaccinated. Given the risk all unvaccinated people face in public places, I think it's in the best interests kids under 12 to remain out of indoor public spaces for fun anyway. School is worth the risk, but a restaurant meal or indoor gym isn't, IMHO.
My kids are both fully vaccinated since Pfizer was approved for those 12 and older but we kept them home before that. They did not go to extracurriculars, they did not return early to school when local schools opened last spring, and they did not go to any public spaces. I made them wait in the car if they wanted to leave the house while I went to the post office or if I went to get groceries. It was a bit suffocating for them, but we hosted regular outdoor hangouts at our house where kids stayed masked but could talk and get some socialization.
When my girls were finally fully vaccinated, we celebrated by going to eat at an outdoor restaurant. We still haven't eaten indoors yet and likely won't for a long time. They're both back in school this Fall but both schools had COVID cases by day 3. It's not safe even when most people are vaccinated but they cannot do another year of remote school--it was soul-sucking and mentally draining for them. So they wear KN95 masks to school and I'm praying they'll stay healthy. I hope your son and other parents with kids under 12 stay healthy and safe, too.