Essentially the whole problem with housing prices in the US is failure to build housing, largely forced through restrictions on building housing, including restrictive zoning.

“Some of the supply of housing that is permitted to exist is used a short-term rentals rather than as actual housing” may be “part” of the problem, but its a vanishingly small part, in that if you deal with the basic building problem, there would be no actual problem, even if the short-term rental thing continued.