The reality is that the government backs house prices by preventing construction via zoning rules. Japan shows us that 0% central bank interest rates do not affect pricing so long as supply meets or exceeds demand. [1]
If Japan fixed everyone's house at 0% for 30 years than jacked the rates, the owners would be idiots to sell for anything but a hefty added premium as they're sitting on a money printing machine of negative real interest rates. Unless something else is going on like the property having weird upkeep laws that make it tough to just use as is for decades.
[1] https://fred.stlouisfed.org/series/JPNCPIHOUAINMEI