When regulations are reduced to allow more density, the value of the land goes up because its productivity increases. The land can do more now, e.g. hold 10 apartments vs 1 house. The same land generates more rent so developers are willing to pay more for that land.
Meanwhile, the value of housing units goes down due to increased competition among sellers/landlords.
Consider two zoning changes.
1) You are a homeowner and more units are allowed on your parcel, e.g. single-family -> duplex. That increases your land value.
2) You are a homeowner and there is more density around you, but not on your parcel, e.g. apartments are allowed nearby but not on your street. Your land value does not increase. Your home value decreases due to increased competition. (Of course, there may be long term effects like the increased density actually leading to economic windfalls in the area, increasing its desirability, and then increasing your home value.)
So if we take it as an assumption that density increases housing stock, there is lots of evidence that density drives down prices of existing land/home values.
Homeowners don't want housing prices to fall. Ever. They don't care about rent prices (at least, not directly). But renters care about both — obviously lower rent prices are good, but many want to be able to enter the housing market but it's prohibitively expensive.
Perhaps falling rent prices has a similar effect on home prices — the value of buying a home for the purposes of renting becomes less desirable due to lower rental revenue, so prices fall. Not sure, the macroeconomics of housing never made sense to me because it's never as simple as pure supply and demand.
As an example, my wife and I finally decided to buy a house in a fast-growing CA suburb (not in Bay Area). The house was constructed in 2021 and sold for $611k. Plenty of renovations have been done on the house, we'd estimate around $20k+ worth of renovations, and the neighborhood and surrounding area has only grown since then (more parks, housing, great schools, stores etc).
The house was listed for sale at $600k; even then we were able to underbid and get our offer accepted. Inspections turned out clean, just minor cosmetic issues.
I don't keep an eye on the rental market but we've lived at two different rental properties and both of those places went up in rent once each, so I can only assume that rent is going up everywhere in this area.
Point is, rent and real estate don't always go in lock step.