They almost certainly do. There were rumors of a Chinese student ban during Trump's last tenure and I remember reading news stories (https://www.insidehighered.com/news/2018/11/29/university-il...) about universities having insurance policies to protect themselves from revenue loss. There should be enough Americans to fill the empty seats so it makes you wonder if university finances rely on international student tuition. So you would expect that to translate into admissions changes.
Reading other comments on here it almost seems like people feel it would be bad if American universities like Harvard had more Americans. Like there is something morally wrong with that. So that's probably a factor also.
If you have ever seen the inner workings of a student hiring committee, you would not say that Chinese students are given a leg up.
Yes, they generally pay more. However, there are so many highly qualified Chinese applicants that universities generally hold them to a much higher standard, in order to avoid admitting "too many" Chinese students.
This is all a function of China producing many more highly qualified students (at the high-school and undergraduate level) than the United States does. If everything were done purely according to academic merit, there would be several times as many Chinese students as American students at American universities.
Harvard is one of eleven American universities that practice need-blind admissions even for international students, meaning that students are admitted without regard for their financial status (i.e., no explicit preference toward richer students who can pay more tuition), and that financial aid covers full demonstrated need for all admitted students.
https://en.wikipedia.org/wiki/Need-blind_admission
Well, I'll be darned—that's... quite something. I can understand why the university felt it had to take that step—perhaps even a wise move, all things considered - but I must say, it certainly doesn't look good.