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I don’t understand the housing market.

House prices have zoomed far beyond what middle class people can afford. Home prices for an average home almost everywhere in America, are far beyond the average incomes of people would would buy those homes. The average income household cannot qualify for a mortgage in an amount needed to buy an average house.

It seems unsustainable long term, that this can continue. Who is buying all these houses at such inflated prices?

My time in Madison ended in the late 1990's, but I can see from 1400 miles away that there is a new component in the local economy that did not exist in my time there. If you were looking for highly compensated positions in Madison in my day, you quickly came to the conclusion that you needed to look elsewhere. There were career paths in state government and the University, and a few private sector employers, but not so many that were highly compensated. Now, Epic and Google and some others in the long delayed private-sector tech extensions of the UW's research are creating something that did not exist before. Young, high-income private sector employees. That explains the high-rise condos on East Washington Avenue - which were car lots in my day there.

What was not mentioned are property taxes, which in Madsion and surrounding communities are astonishingly high. In FL I have a home that has a present market value essentially equal to the market value of my last home in the Madison area. Here in FL the property taxes are approximately $3800/year. In Middleton Hills, same market value home - nearly $14,000/year(!)

People vote with their feet for a lot of reasons. The high property taxes, extreme narrow mindedness of the political environment in the city, and narrow career paths (in the 90's) expelled me like being shot from a canon. Now, what may be retaining some is the presence of new employment sectors that pay extremely well (I'm thinking of Epic, but imagining that Exact Sciences, Google, and others I have missed are paying large $$ to young people, and they are staying.)

“Who is buying all these houses at such inflated prices?”

The biggest new factors are major “investment firms” buying single family homes in large quantities.

They are confident that with their lobbyists in DC that it will be “heads they win, tails the taxpayer loses” so that makes it an easy bet.

Invitation Homes. Blackrock.

Huge investment funds are buying single family homes and turning them into permanent rentals. Some may be fronting for China’s national investment fund. Anyway that is what has been outbidding individuals trying to buy homes. There’s probably no way that this will stop.

I would suggest you watch videos on YouTube by a guy who calls his company Reventure Consulting. I have no relationship to him whatsoever. I discovered his videos about a year ago. He was the first to call a top to the general US real estate market.

However, ALL real estate is local. So, IF people can afford a house in San Jose, CA it has very little to do with what a house sells for in Madison, WI.

Case/Shiller developed a index about how real estate was affordable based on what the average income was in the metro area. This guy at Reventure Consulting breaks it down by county/metro area. So, while Nashville’s real estate market has already gone down 30% form the top and Boise is down 20% from the top other markets like Manchester/Nashua, NH have continued to go up.
As have markets like Oklahoma City, Louisville, Richmond, Myrtle Beach, and several others.

What he points out are the markets that have boomed over the
last 5 years and have gone up faster than people in that area can afford. Again, some of this has to do with Baby Boomers retiring and moving south. Which is why places like Tampa and Miami continue to go up even though prices are very high in comparison to their incomes in their respective areas.

Real estate markets take more than just a couple quarters to come down. It took five to ten years to go up. It will take 2-4 years to come down.

“The average income household cannot qualify for a mortgage in an amount needed to buy an average house.”

In the 2008 period interest rates shot up for about one year according to my old stock brokerage statements I scanned into my PC.

Don’t expect a $100,000 discount because of a temporary interest rate spike.

Who is buying all these houses at such inflated prices?

Let me rephrase your question to "Where are all those aliens pouring across our southern border going to live?"

In Northern California houses in the not so good part of town are being rented to large groups of illegal aliens for insane amounts of money. A 3 bedroom house can house 6 or 7 families. Mattresses on the floors of the garage, living rooms and dining rooms. You can tell where it is going on by driving around on trash pickup day. I put my trash out one night and the can was half full. When I went out to go to work at 6AM it was overflowing from a house (barracks would be more accurate) up the street. Many single family houses are being kept off the market because the owner can make a fortune right now playing this game.