It is likely that high mortgage rates are causing existing homeowners with low interest rate (3%) mortgages to stay in their current homes rather than buy new houses which would require taking out new mortgages at 7%. This means that the supply of homes for sale is very low which drives up the price.
Note that the supply of homes is usually measured by "months of inventory" which is calculated by asking "at the current rate of sales, how many months would it take to sell all the houses currently for sale?" In the graph below, we see a negative relationship between months of inventory and the change in house prices. When months of inventory is below 6 months, prices increase, and vice-versa.
Currently there are four months of supply in the US. But market definition matters here. Most real estate markets are local, so it would be best to measure months of supply locally.