Answer: What do UX designers just “get” that other people don’t?

Empathy.

One of the greatest things a good UX designer taps into is empathy. And this comes out in many ways.

Empathy for the end user, the person who will use the product. How can I help them or make their life easier?

Empathy for the developers. Can I reorganize my approach here so the developers have a reasonable path.

Empathy for the business. This isn't art and this isn't a portfolio studio, I need to help the business win.

From there it's all knowledge, practice, and hard work to make some incredible work.

Cheers to your future experiences!