Shelter and wages are the two core sticky categories of inflation. You don’t negotiate your lease or employment terms every month. Even if there is a change in supply/demand dynamics, it won’t be visible in the market immediately.
This is also why the Fed has been trying to engineer a soft recession. As long as labor markets are tight, there will be sustained wage inflation. And as long as there is wage inflation, there will be people willing to pay higher rates for longer.
The dominant unspoken narrative in the financial markets is that the Fed will overplay its hand and cause a hard recession, at which point they’ll reverse their rate hikes. And when that happens, all the money sitting on the sidelines will reenter the market, leading to sustained inflation. No one really thinks that this beast can be tamed so easily.