You seem to be confused, and a tad ignorant too. Public housing investments are nothing new, and Barcelona has already benefitred from a massive urban development program at the turn of the century.
https://en.wikipedia.org/wiki/Eixample
Barcelona has already one if the highest population densities in the world. The examples you listed in Austria are already eclipsed by the massive appartment blocks in Barcelona and neighboring municipalities. Your average city block in Barcelona is already 6 stories high or greater. It's a dense urban area covered by massive residential blocks.
Even if you start demolishing blocks to replace them with hongkong-style skyscrapers, you would need a few decades to increase supply in a meaningful way, and even then the impact would be negligible.
Barcelona's problem is not supply.