If I’m working on a senior research project in high school, should I talk about that in resumes and supplemental essays?
If you feel that it’s meaningful work to you and you’re not just doing it for a grade in a class then I’d say go for it. Especially if this is self-driven research (i.e. research you’re pursing on your own time with say a local college professor or something like that) colleges can see that you’re motivated to delve into what interests you. I’d don’t know how much you could write about it in an essay unless you tied it make to something bigger than just “my research project”, like what you learned for example or how you overcame a hardship, but some colleges do let you attach research papers/supplementary documents that are non-curricular (i.e. not for a class/grade in school) to your application–that would be a good place to put your research output.
HS students doing major projects aren’t a big deal in many cases (ask an IB diploma candidate about their “extended essay”). If it’s particularly meaningful to you, try to weave it in. If it was part of actual academic research (i.e. destined to be published in a peer-reviewed journal (not the hack pay-to-publish faux science journals)), then include an abstract. But you seem to be referring to a large HS assignment, right?
But don’t feel compelled to nor feel that it’ll make you stand out per se. Good luck.