Around here, it's not really linked. The heat of the apartment market is directly tied to the projected ROI, based on the demand of rental properties and the demand of rent itself. Like Bitcoin mining, sometimes the ROI gets really low or even negative in the short- or medium-term. The friction between the two factors tend to warm or cool one of the markets, but it takes times.

Consider/remember this. Many landlords aren't paying a mortgage, and don't need to tie rent to "a house's value at the time of purchase". They still profit when rent is below the average mortgage, or if rent is well above it. The only thing they care about is maximizing profits regardless of how full/empty their units are. Similarly on the renting side is lifestyle renters. They don't rent "because I can't afford a mortgage". They rent because they don't want to be tied down. They aren't ready to settle and might or might not move 1000 miles next year.

Those two categories are fairly numerous, and both present forces that influence the rental market independently from the purchase market. It means that places with less long-term demand like Detroit, Philly, or Houston have ownership TCO far lower than rent rates. Flip-side, there are just as many cities on the other side of the spectrum. The average rent in Austin is $2000/mo cheaper than mortgage payments on a starter home. In San Francisco, that difference is almost $3000/mo.

The rent is rent. It doesn't have to cover the mortgage all the time. It's not like someone rent is locked in for 30 years. And some bigger businesses will take the hit knowing the appreciation of the house will catch up or know they will buy a majority of the houses in the area and then raise rent that way to eventually be higher than the mortgage.