It’s going to take $5-10 billion just to move SF’s Caltrain station over by like five inches. You’re being wildly optimistic about what you can do with $100 billion.
But you have to have enough coverage to make the system usable. Building one subway line through Palo Alto doesn’t do you much good because people will still have to drive to get to the stations (and because jobs in the area are so spread out, drive on the other end to get to jobs).
In Manhattan, there are 4-5 lines across a strip 2.5 miles wide. Half a mile is about the most people will walk to the subway at each end. You could cover the core of most of the South Bay cities with 5-6 lines. That’s 240 miles of track for the South Bay. At a billion dollars per mile for the subway, that’s a quarter trillion.
That gets you the physical infrastructure to make transit feasible. On top of that you need to topple the local governments so you can massively upzone the strip around the subway lines.