I gather it's a way of saying it's climate controlled, i.e. heated or cooled depending on the season. I suppose as a contrast to calling any semi-random outside space the largest reading space.

Not in the original title, so either it was removed over there or extraneously added over here.

Merriam-Webster says that "climatized" means "acclimated" so I don't think it makes sense as used here.

Not entirely extraneous; the second paragraph of the page begins with "The library boasts the world’s largest climatized reading space and China’s largest load-bearing glass system[...]"

I assume you were joking about a building being so large it has its own microclimate, but I have been inside a building that has its own rain clouds. The building housed a styrofoam factory.

It was always hot and humid in there, probably due to the manufacturing process itself, but not uniformly so. Certain spots would be extra humid, which would cause water vapor to rise up to the ceiling. There were enough particulates in the air for it to then condense into droplets that looked like clouds, which would then create a very light drizzle 20-50 feet away.

I fucking hated that place.

The styrofoam wasn't negatively affected by the moisture?

I am not joking about this, I was specifically thinking of the building NASA puts rockets together in before launching them. It's infamous for this sort of thing.