6.5x54R and 9x54R were manufactured in Russia since, I would say, late 1960's. 9 mm was intended to be a pure hunting round (SP only) for whacking angry/hungry siberian bears and tigers, and 6.5 mm was a sporting round (FMJ only), made for some really good looking heavy barrel MN action based sporters (scoped or with peep sight), don't remember the brand, but those were exported mostly to Europe and used in domestic special target shooting.
5.7 mm doesn't look like a russian creation to me, but 5.45x54R, if it were developed, would certainly be the one. Could be a ultra high velocity thing (3,900-4,000 fps), I guess, if it ever existed.
5.7 mm is not a Russian caliper, more like Northern European...
8.2 mm and 9.3 mm is likely a Finish development, but I'm not sure.
It's absolutely beautiful thing. I now recall I've seen one in person, many many years ago, in the gun room of the shooting club in Moscow, where I've used to improve
my bad shooting skills. Anyway, it was intented to hit dead on with peep sight at 300 meters.