So far you have not really told us anything that would pick Yale out from a very long list of colleges, some similar to Yale, some quite different. To me, the important first question is whether Yale is a good fit for YOU, not the other way around.
I note I think a lot of people with your background do not start this process aware of how complex a question that is in the United States. In most countries, there is way more standardization of colleges and college programs. In the United States, we have a truly unique range of choices–but also often staggering costs by non-US standards. Fortunately, you have found a place where many people are willing to help.
OK, so one immediate question is whether Yale would be affordable for you.
A second immediate question is based on the observation that while Yale College is very good for science and math, it is not one of the top engineering colleges in the United States. So academic fit is going to depend on which letters in “STEM” apply to your interests.
Assuming Yale would be a good fit for both financial and academic reasons, again, many other colleges might be too. So, now a bunch of other things come into play.
Yale College is a medium-sized liberal arts college embedded inside a private “R1” research university. See here for what that means:
That is a popular form for US science/math students, but there are many others. You could do a standalone liberal arts college, which would usually be much smaller. You could also do a liberal arts college/school embedded in a public R1 university. You could also do a more STEM focused college, and those again can be standalone colleges, embedded in private R1 universities, or embedded in public R1 universities.
I really should just stop here, because until you address these questions (at least for yourself), we don’t know whether Yale would be a good fit for you at all. You might well not even apply to Yale. Again, this is the sort of thing that might not even occur to people unfamiliar with the US system, but there are many families in the United States who have been going to college for multiple generations, and they do not necessarily always encourage their high-achieving kids apply to Yale, or any of its close peers. Because for their purposes, different sorts of colleges may be better suited for those kids given their attributes and goals.
But I do want to leave you with one final source of important information.
So suppose you have decided a liberal arts college embedded in a private R1 university is the right form for you. Yale is certainly a very good version of that, and suppose you have determined it would be affordable.
But are you a good fit then for Yale? Would you be a better fit somewhere else?
To help assess this, you can look up the “What we look for” (or equivalent) page available at most colleges’ admissions website. And here is Yale’s:
https://admissions.yale.edu/what-yale-looks-for
Make sure to click through and review all the different subsections.
And then if you read all that and think, “That sounds great! That sounds like they are talking about me, that sounds like a community I want to be a part of, that sounds like an application process in which I can shine!,” then perfect. You may have found a great match.
But you should also check out a lot of other colleges’ pages like that. Because you might start finding yourself thinking, “You know, in retrospect, Yale sounded pretty good, but this one sounds even better! They seem to be even MORE be talking about me, this sounds like even MORE the community I want to be a part of, I think I would shine even MORE in this application process . . . .”
And I would strongly encourage being open-minded about where that might lead you.