1) There’s listing inventory and then there’s housing supply. Listing inventory may go up with increased rates and that could cause a small short term dip in prices, but overall housing supply is low and that will prevent a crash (but see #3). The people listing their homes will generally need to buy or rent a replacement home.
2) The median income person/family is not necessarily buying/renting the median home. This is due to lack of supply, people owning multiple homes, etc.
3) I agree that if people start losing income/jobs on a mass level, that could change things, but it would have to happen on a mass level given the critically low housing supply.