There’s no more proof than any other dish. It’s so popular that no one bothered to have a “protected origin” certificate.
Yet they predominantly are served in this region so having them being “ruskie” or “ruthenian” (a huge region) is much more fair than naming it Galician.
Is there any definitive proof behind that? My family too come from former Polish territories in Ukraine.
It feels like in the last decade all of Slavs have been rushing into claiming as their own many traditions. I find it sad and unnecessary.
In fact I suspect the dish to be popular to move of the former Kievan Rus' region and I know for sure potato and cheese vareniki to be very popular in Belarus and western Russia.