There's a few things in your post. First, are there/were there Jewish populations in the various nations of the former USSR (beyond Russia). Second, could the local cuisines be influenced by Jewish foodstuffs. Third, and this was not implied in the original post, but makes sense too, are the owners of the Georgian Bakery Jewish (hence the Jewish fare).
So, first, yes, there are/were Jewish populations in places like Uzbekistan and Georgia. The Uzbeki owners of Russian Tea Time in the Loop are Jewish I believe. In NYC, there are several Uzbeki/kosher restaurants. At one time Bukhara has a large Jewish population (long gone though). Our tribe gets around. Although there were places like the Ukraine that were traditional pretty closed off to Jews.
Second, obviously there is interaction between cultures/peoples when it comes to food. So much of what is considered "Jewish" food, is food of Russia, Poland, Germany, etc. I mean I was at Grota, the Polish buffet last night, and there were blintzes and latkes. It would seem, as the lawyers would say, ipso facto, that the influences work both ways.
Third, are the owners of the Georgian Bakery Jewish. I am pretty sure not. But there is a curious relationship between religion and a lof of the more recent (last 20 years) immigrants from Russia and related areas. As people may or may not know, the USSR ruthlessly discriminated against Jews and did their best to try to destroy the religion in the USSR. Many Jewish people who remained in the USSR stopped practicing or even identifying with their religious past. So, when these people came to the USA, their Judism was not exactly strong--hence the various hams and related products at the Russian deli's. On the other hand, as the immigration laws gave certain benefits to Russian Jews, more than a few Russians came to the USA masquerading as Jews. It does blur things.
The way I look at it, the Georgian bakery and some of the other stores around there, like 3 Sisters, are some of the more interesting chow we have. What ever the religious issues, it leads to good eating.
Rob