Should one add a "research statement" in their CV
A research statement is usually a longer document describing what research you did, why you did it, why it's important, and what you want to do in the future. While your CV should just be about stating the facts about your career, your education, achievements etc. So, no, I would not put a research statement in a CV
However you should add a section listing your research projects (completed and ongoing). Example:

(2019-2020) 3rd year Bsc project: Designing a new algorithm to do X.
(2019) Summer project: Built a web app to do Y.

If you craft the description right, you can explain very succinctly what you did, without it becoming a research statement.
Don't worry about the length of the CV, you are applying for a PhD so it's expected that it won't be very long.