I don’t foresee prices recovering in a significant way. My apartment complex wanted an additional $300/mo rent for a yearly renewal and no matter how strong of a recovery there may be on the horizon, I sense higher prices are mostly here to stay. From a business standpoint, a perception of high inflation is the perfect cover for raising prices, especially if it seems like everyone else is doing it. Plus, assuming costs do go down again, you can pocket the difference rather than lowering prices just to need to raise them again for inflation later.
I think it's more complicated than that because that trend has been going on for a long time with no connection to inflation or even supply chain snafus. Fixing it is going to require changing a thorny mess of policies constricting adequate housing construction, density, redevelopment, etc. and private investors piling into housing as a revenue stream. Housing really looks a lot like what you'd expect where there simply isn't enough supply for market forces to keep prices in check.
That’s a good point. I am also a strong believer in the maxim: “Landlords are greedy”. So in that sense the dramatic rent hike can partially be attributed to inflation, but also due to the simple fact that they can.