I know that Ukrainian is a new ethnic term. Russian (russkiy) is also a new term. Between 1795-1917 there were three artificial ethnic terms

Velikorusy (present day Russians)
Malorosy (present day Ukrainians)
Belorusy (present day Belarusians)

Russians and Ukrainians changed their ethnic terms after WWI. Belarusians kept it.

People of eastern Galicia (western Ukrainians) were part of Austro-Hungary, so they kept original ethnonym Rusyn.

Every sane person considers Rusyns eastern Slavs who speak an eastern Slavic language. Rusnaks of Slovakia and Rusyns of Voivodina are also eastern Slavs, but their languages are influenced greatly by Slovak language.

Greek Catholic are originally Orthodox who were converted into Greek Catholicism after union of Brest (1596) to be in jurisdiction of Vatican https://en.wikipedia.org/wiki/Union_of_Brest

I accept modern day people can be of any religion – Roman Catholic, Greek Catholic, protestant. Originally, Greek Cathoilic were Orthodox who were mostly eastern Slavs. Unless you can show me that Slovaks (Moravians however your ancestors identified themselves 1,000 years ago) accepted Orthodoxy.