I’m not sure you can get a visa for Harvard Extension and I don’t think they offer full scholarships.
My guess also is that you say “Harvard” as a default for “world-class university”, of which there are many in the US (there are 3,700 universities in the US and even the top 10% are excellent but aren’t likely known in Europe.) If you’re willing to look at more than Harvard, we can help.
Is University of the People a “real” university that grants ECTS (European-validated) credits and bachelor’s degrees to people who graduated high school with good marks, or is it a “university” in that it teaches many classes and seminars, for people who wish to learn?
The distinction is VERY important for US colleges, since if the former you’d be a freshman applicant, with one hundred more slots open than if a transfer and full scholarships offered if admitted; if the latter, odds are really low you could transfer into an Ivy+university because so few freshmen leave and so there are so few spaces open, and even fewer for internationals who need financial aid (as for most universities, they wouldn’t have financial aid for international transfers).
Also, are you a woman or a man? (Women’s colleges have a mission for non traditional age women whose life interrupted or prevented college).
As you know the Turkish border has opened; Germany, France, Sweden, have free-tuition universities.