Yea, the dictionary definition of a republic allows this country to be called a republic, given a reasonable amount of leeway for the specifics. It’s a democratic republic, but the adjective “democratic” is not the noun which names what this country is: a republic, and Federalist 39 gets further intonthe weeds and calls it a “compound republic”, (which is so right).
Also see federalist 51, for “compound republic”