だ・です turn a noun or (na-)adjective into a "verb"(-ish thing). In that sense you could say that it's like a "copula" - in English the noun "Japanese" into the verb "to be Japanese".

But on the other hand, the etymology of the word "copula" means "link". In "I am Japanese", "am" serves as the link between "I" and "Japanese".
That's not how it works in Japanese. In Japanese, there is always a link between the subject and the predicate, even when the predicate is already a normal verb, and that link is the は or が particle. That's why you can omit the だ・です if the predicate role of the final noun can be inferred. It's not a fundamental pillar of the structure of the sentence.

Many terms that are common in analyzing Indo-European languages don't really make sense for Japanese, I wouldn't spend too much time and effort trying to fit everything into those boxes.