In the US, people have been complaining about this for 100 years. I haven't found any successes yet. I suspect it's because it's a demand problem, not a supply one. Make high-demand areas less attractive and low-demand areas more attractive.
Places where many people already live will always be the most attractive. You are not going to solve this by trying to even out population density. Trying to manipulate demand with anything is almost always a losing approach.
You don't have to overcomplicate things. Supply less than demand > price goes up. Increase supply > price goes down. The data shows the same pattern over and over again[1]. See Japan as an international example or Minneapolis[2] and Austin[3] as US examples.
Those are the three examples everyone uses, but I thought those were pretty weak so I didn't include them. In fact, I was curious enough that I looked up comparable homes to mine in both Austin and Minneapolis, and the house prices were practically the same.
So, 100 years, and three weak successes (if you can call them that) - doesn't sound like a winning strategy.
A demand view gives other routes to explore, at least.