Skovoroda was writing in a bookish Slavonic language learned in Kyiv Mohyla Academy. It was a direct descendant of Church Slavonic, which is a derivative of Old Bulgarian (which Rus adopted along with Christianity). All educated people of ex-Rus learned it and used it, it was an official language of the Hetmanate state. It was like a Latin for Western Europe in Medieval times.
As per Ukrainian classical writer and researcher Nechuj-Levyckyj, literature Russian language was initially created by Lomonosov, who learned bookish Slavonic in Mohyla Academy. Lomonosov mixed that bookish Slavonic with Moscow city dialect as well as created a lot of terms by himself. That's why it's not surprising that Skovoroda's Slavic language looks more similar to Russian — bookish Slavonic is a base of literary Russian.
Literary Ukrainian, instead, formed by spoken dialects of Ukrainian people, unlike stillborn and bookish Slavonic. Shevchenko, Kotliarevskyj, Nechuj-Levyckyj wrote in that spoken, real language. Many classical authors made fun of people who were trying to seem more educated while using bookish words, which no one used and anyone hardly understood (e.g. "Natalka-Poltavka" and "Konotop Witch" by Kvitka-Osnovjanenko).
As for Skovoroda, I wouldn't call him a Ukrainian author since he never wrote in Ukrainian. Neither would I call him a Russian author for the same reason. Skovoroda was a cosmopolitan (others would say — Medieval-minded) and used international and kinda dead bookish languages: Latin and Slavonic (btw, Shevchenko criticized Skovoroda for that). Good or bad for Skovoroda, idk, but he did no direct input in Ukrainian literature. The Ukrainian translators of his texts did.
