Did the shift to remote work cause a housing shortage?

Did the shift to remote work cause the post-pandemic run-up in rental and home prices? A research summary from the San Francisco Fed makes the cases that this was a major contributing factor.
"The COVID-19 pandemic reshaped the way households work. Nearly a third of employees still worked from home part time or full time as of August 2022. This has significantly increased housing demand and is a key factor explaining why U.S. house prices grew 24% between November 2019 and November 2021. Analysis shows that the shift to remote work may account for more than half of overall house price increases and similar increases in rents. This fundamental evolution in workrelated housing demand may be important for future house prices."
We moved from about 5% remote work pre-pandemic, to a now relatively stable 30% post pandemic. This is a major shift, and it's had a large impact on housing needs as people now require more space and privacy at home.
https://www.frbsf.org/wp-content/uploads/sites/4/el2022-26.pdf