What Will Happen to Prices Due to Inflation & Higher Mortgage Costs?

Higher inflation increases interest in holding durable assets like real estate. In doing so this also affects the cost of money creating increases; both affect the impact prices.
Interest rates incorporating inflation rates do not necessarily have a negative impact on assets expected to appreciate at that same rate.

Inflation can be unexpectedly low, the case over the past several years or unexpectedly high, as might be the case for the next year or two. The more inflation we expect in the future, the more desirable it is to buy a home now and capture this price appreciation.

If rents or prices grow at rates comparable to, or above, those embedded in mortgage rates, then the impact of higher interest rates may not be negative, especially for assets like single-family homes. If the interest rates increase because of inflation expectations increase, that has a dampening impact on affordability but also increases the desire to hold durable assets as an inflation hedge.