You have to look at the average household size and number of children, not just population.

A world where most households are man + woman + 0..3 children is very different than one where most households are 1..2 people + cat/dog. The latter demands far more housing than the former, even when populations are otherwise equal.

A population of 10 million singles demand 4 times more "housing units" than a population of 10 million people in 4-person families.

This is what makes immigration-driven population growth so pernicious compared to childbirth-driven. The family structures you end up with are completely different.

> A population of 10 million singles demand 4 times more "housing units" than a population of 10 million people in 4-person families.

Those housing units are not interchangeable. Families often want extra bedrooms, and units with extra bedrooms are frequently sorely lacking.

This is one thing that is very strikingly different in different markets. A lot of US metros have a fair amount of new housing but almost none with even two bedrooms per unit, let alone three. In a place like Taiwan, there are similarly absurd housing prices, but the new dense developments have four- and five-bedroom units.

I don’t have any data or links to contribute, but my gut feeling is that this effect would be dwarfed by population movement, specifically urbanisation - if rural areas are emptying out as everyone moves to the city, you can get the same patterns (e.g. reduced housing supply in cities and all the flow on effects from that) without any change in total population.