Where I'm from (EU) experts say that prices will stagnate amd the market will slow down.
On one hand the high inflation pushes out lots of buyers -- they can't or don't want to pay the high interest rates. This lowers demand and prices.
On the other hand global supply chain issues (which got much worse with the war) lead to material shortages and rising material costs. This pushes up housing prices.
The net result is likely stagnation -- few houses are built and few exchange owners. But prices stay high.
Except if there will be a large recession causing people to loose their jobs and unable to pay their mortgages. This will crash the housing market, but looks unlikely now.