I think this is about interest rate on savings side. Ten years ago in Poland you could get saving account paying 7% interests. 5 years ago you could get one that pays 3%. Right now interest rates are almost at 0, and saving accounts pay ridiculous 0.01% interests. Which has the effect of people taking money from the bank and buying apartments, as an investment.

With high interest rates, you might get good return on savings account, but it will make the mortgage payments much higher. Most people prefer to get a mortgage and move in earlier in their lives, instead of saving for decade or two in order to buy house/apartment with cash in their mid 30s or even 40s.

Not only that but if you’re paying a mortgage you’re not paying rent. Buying means your housing cost is now an investment (minus interest, tax, and upkeep) rather than just an expense. Now it could well be a terrible investment, but in theory you’ll own something of value in the end in addition to the housing you had as you paid.

I am assuming those rates aren't adjusted for inflation? Real rates have certainly decreased in the USA, but when we had high rates we tended to have high inflation as well.

Yes, rates were not inflation-adjusted. But in our country it is the opposite: in times when savings account paid 7% we had maybe 1.5% inflation. Now, when the rates are near zero we have 5% inflation. So keeping money in the bank means losing 5% yearly - you can see how that motivates people to buy some real estate.

Increase in mortgage availability is directly linked to price increase.

Yes, but the point is that price increase doesn’t affect affordability if the lower interest rates compensate for it. Why does it matter for affordability that house prices went up 20%, when mortgage rates fell so that the monthly payments did not budge much?

But this is not what happened. Median carrying costs for real estate have fallen, so that US housing affordability has increased (for buyers).

The places where this is not true are all places that have seen significant population growth and have not permitted sufficient new construction. For example, in Jacksonville, FL, the median home costs $250k, which would leave a payment of ~29% of the median household income in Jacksonville using a 5% down payment. Similar math works in other cities where builders have been allowed to keep pace with population growth.