PC: How would Eastern European Jewish culture develop in a world where the Partitions of Poland never happened?
It was mostly because of these partitions that the Russian Empire went from having very few Jews within its borders to becoming the nation with the largest Jewish population in Europe, but they were restricted to the Pale of Settlement.
Now, had the Polish-Lithuanian Commonwealth avoided the partition, would Eastern European Jewish culture be influenced largely by Polish, rather than Russian, culture? Moreover, it would also be interesting to see how a surviving PLC would also have an influence on the development of later Jewish religious movements similar to Hasidism.
I would expect Jewish-Polish intermarriage to eventually become a huge thing in this TL. Also, Jewish-Lithuanian, Jewish-Belarusian, and Jewish-Ukrainian intermarriage. I would also presume that the "civilizing" influences of the Jewish Enlightenment in places such as Germany would eventually spread to the PLC, though I don't know when exactly.