> I'm wondering if UX is backed by science/engineering.
Yes it is and has been for a long time. Time and motion studies were taken throughout the 20th century and even in the 19th. (There was a recent HN posting about such a study in aircraft cockpits of the 40s or 50s and the need for adjustable seating, relaying to air crashes). Don Norman published one of the first great such books (Design of everyday things) — check out the nuclear plant photo!
There was a deep study of the efficacy of design in print media which fascinatingly to be settled on different design points in different countries, though the most scientific such studies waited until computers were readily available.
Early GUIs were controversial and UX studies going back to the early 70s by people like Stu Card and by Fitts have been both surprising and influential. Xerox PARC where Card worked even hired anthropologists.
UX researchers are pretty important today. All the “big guys” (FAANG etc) and less well funded companies as well.
Engineering? Well companies spend a lot on their sites and devices. You can decide on that part.