Canada

It’s primarily the municipalities

Municipalities are a creation of the province, so the province has the same power as municipalities. As this is reported to be a province-wide issue (in most provinces, at least), it does seem like a place for the province to step in.

The province can pass domestic speculation taxes. Municipalities are hamstrung in this thanks to the province. The province limits what municipalities can do. The province needs to do more.

While I agree that it's the municipal responsibility to actually get the zoning laws and passing new developments, it's also the responsibilities of the governments higher up to do something when the lower governments are starting to fuck around.

I imagine that the provincial government is within its rights to force the change of zoning laws so that single residentiary zones no longer exclude townhouses and multiplexes. A simple change that'll have radical effects in the long term, though admittedly limited effects in the short term.

Both governments are able to simply purchase land and build what the hell they want on them as well. Government subsidized housing doesn't have to mean that the government has to subsidize the rent, but instead just subsidize the land sale and force multiplexes and low-rise apartments to be built on them.

It's a brute force method that'll piss off certain groups, but it'll make others shower them with praise as the basics of living become affordable.