SF has a relatively high ratio of housing units to population compared to other cities in the US and a 9.7% vacancy rate. By the numbers, it has an oversupply of housing.
That is not a valid interpretation of the data. The ratio you cite, which is a pointless one, is mostly influenced by household size. SF has a relatively small household size compared to the state and nation. The vacancy rate you cite is also not a useful one that people generally understand. There were 19000 units for sale or rent during the last ACS survey, out of 418000 physical dwellings, and that's only 4.5% which is very low by historical standards.
By just those numbers, sure.
How many are homeless?
What does the median worker spend in money and time commuting from somewhere further?