The problem is not foreign capital but that someone thought that limiting housing construction would be a good idea
This has not stopped housing costs from going through-the-roof. People are buying houses to speculate, new residents (foreign rich, or migrating techies) are buying houses with staggering amounts of money - amounts that existing residents could never hope to save up.
[0] https://komonews.com/news/local/home-prices-dropping-in-the-...
[1] https://www.seattletimes.com/business/real-estate/seattle-ar...