This is entirely dependent on the market in question. Home prices are not a 1:1 reflection of interest rates.
In my Canadian city, where nominal prices did fall due to ballooning interest rates, but not proportionally to increased costs.
This is because:
1. Home sellers still have to live somewhere, and will not be willing to sell and move for a big loss (unless they absolutely have to)
2. There is a belief that rates will come down to reality at some point, even if not as drastically low as the pandemic years.
3. Interest rates do not raise the supply of homes. It’s the opposite in fact. Rental prices continue to increase quite quickly. So even investors are less willing to sell for a loss, as their yields may not have been as highly impacted.