This is my very American-centric view on the housing prices continuing to rise despite high interest rates:
Large investment companies are beginning to leave the Commercial Real Estate sector due to the consequences of the pandemic. While commercial RE was seen as a stable investment strategy, that is no longer the case. The residential market is the new (somewhat) stable investment. Not everyone needs an office, but everyone needs somewhere to live.
These investment companies are now beginning to purchase newly-built communities of hundreds of single-family homes and turning them into rental-only communities. Removing homes from the sale market and locking them behind rentals.
Rental prices are much more stable during a recession or contraction in a market. When the market is great and homes are "affordable", it's still a competition of wealthier, older generations that can outbid those in their 20s or early 30s, locking the younger generation into rentals. And when the market is bad and everyone is getting foreclosed, rentals become more in demand, increasing those rental prices.
My city has built over 1,000 new homes in various communities in the past 2-3 years but they were all purchased by investment firms before construction was completed and they are now rental-only neighborhoods.
The recent prices aren't being lowered due to the rate hikes because of these investment firms. To sellers, demand is still high (they don't care whether the buyer is a person or a company), so why lower prices?
EDIT: This is specifically noticeable in suburban metro areas due to the higher average income of residents and the high demand for housing.