Strictly speaking, as more and more skyscrapers are built on the surface of the earth, does the day tend to become longer or shorter?

the day tends to become longer

Explanation:

Places in high elevation like Skyscrapers tend increase the radial distance from the spin axis of the Earth. So when you are physically on top of a skyscraper, The rotation of the Earth will feel a tiny bit slower compared to those who are in lower elevation.

That's being said, the difference doesn't really matter. Almost Irrelevant. Most skyscraper will only make the day feel longer by a fractions of seconds.