Mission bay and soma are the two places where residential is being built but it’s all expensive high rise esque units that middle income can not afford.
The only other way to deal with the mismatch of shortages is to have waiting lists or lotteries. Both of those are used for subsidized housing in SF, and the lotteries are ridiculously lopsided, to a tragically comic degree.
The only people who benefit from the shortage are landowners, and boy do they take it in.
I grew up in the bay and now live elsewhere because the price of living in the bay became unjustifiable to me. I don't see why so many people feel that they are entitled to live in a place that they do not own and feel its the role of the gov't to ensure that they have a place to live.
Those of us who live here do not exist as islands. We all participate in a rich economic web that requires exchanging services with lots of people. Teachers, bus drivers, delivery people, shop keepers, mechanics, plumbers, police officers... it takes a lot of people to run a society.
Typically the "not everybody has to be able to afford to live here" mindset has worked only when there is a wealthy exclusive enclave that tries to keep out poorer people and races they don't like, but when that community can still draw workers from more affordable places nearby.
The Bay Area has taken that "these people we depend upon for our lifestyle don't deserve to live here" attitude and applied it a region so large that people can no longer commute in. It leads to extremely dysfunctional societies.