Governments should simply regulate more so that people vacationing will go to hotels and houses will be available for residents
Berlin did exactly that: You can rent out your apartment for IIRC 30 days a year, or while you're also living there, if you want to rent out more you need a hotel license and tough luck getting one while there's a housing shortage, least of all for a flat in a residential area.
But OTOH that's all only taking the edge off there's been decades of under-investment in social housing in Germany overall, and the little social housing that got built got built via attaching conditions to building permits for private investors, those apartments lose their social housing status after 20 or such years.
And it's not like there aren't companies who want to build, and build plenty -- but they don't because they can't recoup costs, not in this market where every rich fuck who can afford rent already is living somewhere else: Building costs are too high. Some of that is building standards, permitting, etc, but the bulk of it is financing costs, that is, interest on loans for new construction is way too high. Getting at land is not always easy but there's plenty of mechanisms such as municipalities having right of first refusal for any land sale (if they want to, that's another topic). There's really only one way out of this and it's state coffers because the capital market certainly isn't going to get less greedy.