"House-Price" is a terrible metric that only house sellers really care about. Everyone else is more concerned with monthly total housing costs. If house prices stayed the same and interest rates increased 2-3x that means monthly payments for new mortgages also increase. Buyers are unable or unwilling to pay the higher monthly cost so they bid less and the price comes down but their total monthly payment does not decrease.
In some sense this is a transfer of wealth from home owners/sellers to banks/lenders and hopeful and prospective first time buyers see no benefit, aside from maybe smaller down payments.