The problem here is that when interest rates go up, those who locked in historically low interest rates are going to be less likely to sell their homes. Those who have to sell their homes aren't going to reduce the price by 20% just to sell, more like they'll sell at current market prices (which are still way up) or just sit on the house instead of taking a loss or too large of a discount.
On top of that, higher interest rates mean it's more expensive to build new homes. So you get less supply.
My mental model for home prices is that there are some general fluctuations and such but the overall market trend will continue to be neutral to positive and rates will grow as well. The "rates are high so prices must come down" mechanic is far too simplistic and unrealistic.