Building more housing means you go further down the list of incomes. Fixing income inequality reduces the gap between what the person who gets the house pays and what the person who doesn't get the house would need to pay, which makes things seem more achievable (and increases disposable income for people who get the house), but doesn't change who gets the houses. Rent control replaces the price-ordering by time-and-luck-ordering for a subset of the population: some people enter a secondary housing market where they get the house by virtue of being lucky at the time it went on the market. Prop 13 preferences older homeowners over new immigrants (or young people) by effectively surcharging new purchasers. The only two policies that solve the displacement problem are building more housing and making the city less desirable to residents, but other policies can change who gets displaced.
San Francisco is an interesting case because tech tends to have so much higher salaries than other industries. As long as there are enough tech workers to fill up all vacancies in a given housing market, the market-clearing price will rise to a tech-worker's salary, and everyone in other industries will be forced out. How many people can San Francisco tech companies hire? I dunno, but I'd bet it's a lot more than the number of housing units currently being built in SF, which means that some people are gonna get kicked out on the street. The single-family home market in the Bay Area is probably already shot - given the number of units on the market, dual-tech-earner families could easily fill them. But the condo and rental market might be able to be saved; enough building could probably create enough housing there to absorb the tech industry, which would leave units that rent at the price an ordinary worker could afford.
I think it might be interesting also to talk about the quality of housing. You touch on a related topic "making the city less desirable to residents", but I think it's worth adding something to that.
If you segment the housing by housing deemed good enough by people with high incomes, and housing of a quality which they won't live in, you can achieve the goal of allowing in lower income people without satisfying the demand for all of the higher income people (either high income people won't work and live in the city, or they'll commute from somewhere with housing they want).
Additionally, you can lower the threshold for people living in the city to live outside the city by making commutes easier.
This could also be used to demonstrate how replacing old and lower quality housing with luxury housing could negatively impact people with lower incomes, even if you're building more luxury units than there were previously low quality units, since in this thought experiment the market for luxury units doesn't affect that for low quality units (this refutes a commonly posed argument that it's good to build luxury housing as long as it's lots of units).
I can't say for certain that they market actually segments like this, but it's not too hard to convince yourself that it does.
