The solution is to build more, and the success of Vienna does not come from public intervention but from the added supply. Tokyo is another city with famously cheap housing, and the secret is that they make it easy to build.
I personally think that achieving affordable housing prices via mainly government intervention is not a sustainable approach. You end up consuming both economic and political capital.
A more sustainable approach sets clear, transparent rules that specify under what conditions do you get to build by right. Then 90% gets satisfied by the market, the remaining 10% can be addressed by government investments, if needed.
The only sustainable way to get affordable housing is when the market price is affordable.
Land, on the other hand, is another story. There is strong economic evidence that many of the observations of Henry George [1] are spot on: Land rents tend to take a massive toll in the economy, cause inequality and misery, all without requiring their owners to provide any added value. The proposed solution, again with solid economic fundamentals, is to tax the unimproved value of land at 100%. Henry George further argues that the proceeds should be equally divided among citizens, a citizen dividend if you will.
[0] e.g. it takes 4 years on average to get a new building permit in SF, 90% of the city is zoned for single family housing, any neighbor etc.