Plenty of others have highlighted the issues with Commute. I'll just say that the time you lose to commute is not coming back. Your call how much that time is valuable to you. If traffic (both driving and transit) returns to pre-COVID levels, you will be spending 60-90 minutes one way from all those towns you mention (and tri-valley, Walnut creek etc areas others listed). I would pick a home in Millbrae, Burlington, San Mateo, SSF.
The 7th grader will be starting high school in 12 months. It would be best to relocate now so they get one year in a middle school in the bay area to form friendships of which a few can carry over into high school. The 2nd grader has time and will adapt.
The high schoolers in the Bay Area are very competitive (Grades, GPA, extra-curriculars) as they all target colleges 4-5 years out. Just as you will be going through a fast pace at work, the 7th grader should expect to have to work hard to keep up. The good schools have children (and parents) that are hyper focused on colleges and admission. If targeting a STEM field, that has its own pressures. Outside the STEM field, no one really seems to know what other college majors lead to in the Bay Area. That's what you get from the intense tech focus of the parents.
When picking a city/locality to live in, definitely research the public school's finances, teachers, student-teacher ratio, budgets. Private schools cost a pretty penny (12-23k p.a. per child) and have competitive tests to clear to get admitted. Public schools and their school districts continue to suffer from funding gaps that puts pressure on the parents to supplement what is taught in school with private lessons (which is a separate cost).
Things might change in the next 4-6 years with the SAT and ACT evolving. But if those are still in consideration by colleges, expect to pay to take practice tests to chase that high SAT/ACT. Those practice tests etc. can add up to 3-5k p.a per child, not counting any counseling you might engage with for college essay prep, guidance. Private schools provide better quality counselors, removing the need for a separate external counselor.
Also consider how you might be impacted if state voters bring back affirmative action in admission to state colleges.