I'm a developer with a background in design. In my career I've built and maintained UI component frameworks in SCSS and React, built web apps, and collaborated with designers and product owners to improve the app's UI and UX. As the builder of these products, I'm usually the first one to actually experience the them, so I'm in the strongest position to notice problems and suggest improvements.
So, yes, there is such a thing as a UX/UI developer/engineer.