Still, I fear that people generally look to politics for simple, one sentence solutions to problems which take decades to manifest.
Barcelona is the 68th densest city in the world. You look at a satellite map and you can see they have a very well planned city layout. It's dense and filled with tall buildings.
At some point the only lever left to pull is outright banning of foreigners. I'm not condoning that policy - just trying to highlight the futility of attempting to protect a desirable area from overpopulation.
That does not follow at all. If you look at the actual densities Barcelona is 1/3 as dense as the densest city in the world. There is plenty of room to accommodate more housing, they just need to build higher.