The solar covered parking lots near me are great because they also serve as cover for your car when it’s hot and sunny.

It’s not the most cost effective way to install solar, though. A tall structure designed to put the panels high up in the air and leave a lot of space for cars is a lot more expensive than normal rooftop solar or even field setups. This is basically a way to force some of the cost of clean energy as a tax on parking lots. Which may not be a bad thing for dense cities where parking lots have their own externalities on the limited available land.

I wonder if this will make it preferable to build parking structures rather than parking lots.

The lot is always cheaper, as long as the land is cheap. And in most of the US, even land that isn't all that cheap is often best left as a parking lot, economically: You can easily speculate with a parking lot with minimal investment, as the taxes for the empty lot are often low. See all the midwestern cities whose downtowns are 30-40% surface parking.

There are all kinds of bad externalities caused by seas of asphalt that is unused 95% of the time, but few countries are all that interested in using any mechanism to make the property owner pay for them.

I imagine land is more expensive in South Korea than in the US.
Because they do things like this (Green belt).
Because they have a population density 5x that of the US.
We're comparing cities though. Seoul and Manhattan are comparable because they both have features that prevents sprawl.