House price is inversely correlated to interest rates BECAUSE most buyers are getting a mortgage. So the price of the house "will drop" (hard and fast estimate here not a law) if interest rates rise because people are paying for house+interest = total_cost_able_to_pay.

I watched this play out in real time as I purchased my home. Rates dropped, prices went up to fill the gap. Owner got a bit more money vs the bank instead.

Basically I gave my money to a different person, but the "all in" was about the same.