I’ve written extensively on this subject over the years. The principal reasons for soaring rents are: increased demand for low-density housing in somewhat remote areas due to the pandemic; the loss of construction workers after the Great Recession; rising materials costs; and overly strict, or at least poorly structured, local government regulations.
The first of these reasons has already started to ebb. The third can’t really be controlled by any level of government. The second could be addressed by encouraging immigration and by providing better vocational training opportunities. The last is complicated, but the key is to give neighbors incentives to support new housing projects instead of reasons and pathways to oppose them.