Housing affordability is a huge topic, so there's a lot of it there on this. Since, you didn't say what country you're interested in, I'm going to go ahead and assume the U.S., because that's what I know. I imagine many of these sources have correlaries in other countries though.

Many of the variables you listed are available through the U.S. Census Bureau's American Community Survey (population, income, housing prices, rent burden).

I'm less familiar with it, but FRED Economic Data may be able to give you more information on the interest rate side.

Housing supply and construction can be trickier to get at. A lot of places track new construction but it's often behind a paywall -- and this is often tracked by real estate professionals so there's sometimes some bias built in. The Census Bureau has a report on New Residential construction, but I haven't found it overwhelming accurate when you get down to the smaller geographies. If you have a specific place you're interested in, you may be able to get information on total residential buildings/units from the local assessor's (sometimes auditors) office. Building permits are often used as a proxy for new housing construction, though it often requires some careful cleaning, and may be publicly available from the local gov's building/planning department. A lot of states and municipalities have data portal websites which can usually be found by googling "(place name) open data."

Or if you just want some stats on American housing, Harvard has a commonly cited report: https://www.jchs.harvard.edu/state-nations-housing-2022

Though there's a lot more out there too. Good luck!