Depending on which group of immigrants your parents, grandparents or great-grandparents arrived with, most were considered "Russian" because that was the country in most of what the Pale of the Settlement was considered. My dad's grandparents were from Podolsk, Ukraine and Minsk, Belarus; actually, only one was from Podolsk, the others were from shtetls outside those cities. When they came to this country, they only spoke Yiddish and Hebrew, though the latter was not really spoken per se. They didn't speak Ukranian, Belarussian, or Russian, though one great-grandmother did, and it is likely the other did too. Women generally spoke the native tongue for the area and Yiddish, the men generally only spoke Yiddish.
There are a number of Jews who are rediscovering their roots in these "new" countries. However, their forebearers usually only considered themselves Jewish, which is why it is doubly sad the number of Jews who don't even claim that part of their heritage; well, unless they are called upon to criticize Israel or some other Jew.
I can't say I feel an overly personal connection to Ukraine or Belarus because we weren't raised knowing those countries, and even with the new information, when it came to Jews, they were generally not thought of as anything other than Jews. There may be some cultural overlap, but a "Ukranian" Jew would have more in common with a German Jew, who wasn't bougie, than a Ukrainian Jew would have with a Ukranian. The current situation, in both Ukraine and Belarus, have been on my radar for years now because of the new revelations, but it is more out of historical interest, not as much as personal connection.
Jews of the Pale are rather unique in many ways and differ in their experiences than the Jews of Western Europe and Russia proper. Of course, now, we, like many minorities, are all treated as singular, hive-minded, and monolith.
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