As others point out, the discipline is called Human-Computer Interaction and has a rich history. The best example in the field might be work on Fitts’ Law, such as https://www.yorku.ca/mack/hhci2018.html

For more practical examples of how websites can be redesigned through science, though, see https://www.nngroup.com/ and other resources online regarding scientific study of UI, user experience (UX), etc.