The issue here is as you can see on the map, a lot of these areas are not currently part of Poland, and many of the people living there were not necessarily culturally Polish to begin with.
As Sarny (unlike Vinnytsia) was part of Poland between 1921 and 1939, if you can document in any way that this great-grandfather lived there around that time you may qualify for some sort of ctitzenship track or special immigration status. Knowing the language is secondary in such cases.
TBF, I suspect that most Polish Jews were not culturally Polish right before the start of the Holocaust either.
Well, my Jewish great-grandfather was born there, but he got forcibly kidnapped by the Bolsheviks at gunpoint during the 1919-1921 Polish-Soviet War. Yes, seriously. He had to leave his parents and siblings behind in Sarny. The Bolsheviks took him hostage because he was literate and unmarried and they felt that they needed someone of his skills. That's what my dad told me, and that's what my dad heard from him himself back when he was alive (he died at age 88 in 1985). So, Yeah, after the Polish-Soviet War, he ended up in Central Ukraine, where he met and married my Jewish great-grandmother and after which point they had two sons. Ironically, him not staying in Sarny significantly increased his odds of surviving the Holocaust since he and his family were able to get successfully evacuated from Vinnytsia during Operation Barbarossa, thus saving their lives. They initially went to Stalingrad and later on to Samara (Kuybyshev) Oblast after the Nazis were approaching Stalingrad. Most of his family who stayed behind in Sarny got murdered in the Holocaust. Only a brother who moved to Israel in the 1920s, another brother who successfully fled to the Soviet interior in 1941, a cousin who successfully fled to the Soviet interior in 1941, and a nephew who successfully fled to the Soviet interior in 1941 survived. Though he also had a sister who moved to Argentina in I think the 1930s and who died in childbirth giving birth to her first child. Her son survived and later moved to Israel, where he apparently became a semi-famous architect.
As for proof, I'll see if I can find anything, though my last name is very rare and anyone who has even a basic knowledge of it will know that it originates from the Volhynia area. It's obvious enough by the fact that a lot of Jewish people with my last name were murdered in the Holocaust in the Volhynia area.