At least one of Chekov’s “Russian inwentions” is attributed to someone from Minsk, which is in modern-day Belarus.
Leningrad’s cloud cover rating is given during the disaster scene in Star Trek IV.
And a dedication plaque for the SS Tsiolkovsky in Star Trek: The Next Generation gives its construction as taking place in the Baikonaur Cosmodrome in the USSR (modern-day Kazakhstan). That means that in the Trek universe, the Soviet Union existed at least up until 2364. (Or perhaps it was restored sometime between 1991 and the 2260s).
On the other hand, the Trek universe is already a full-blown alternate continuity from our own, since they had the Eugenics Wars (which included the rise and fall of Khan) in the 1990s.
To be fair, it is, like every other entertainment universe, an ‘alternate universe’ where the laws of physics are clearly different from those in our universe.
In a way, that is what we have now, except that it is now called Russia, and is a little bit smaller. It is still huge, and still ruled by a former Soviet official. (And, of course, it was very often informally called Russia, even when it was the USSR.)
I’ve been reading Russian Spring and its quite an amazing novel even with its rather ridiculous sibling Cold War (with one being almost completely Americanized and the other Russianized) and all the characters having sexual lives resembling that of Hollywood movie starts. While some of its specific predictions were obviously incorrect, its picture of American society and government policy is spot-on while the secessionist movements toward the end of the novel foreshadows the collapse of the USSR albeit delayed massively. The most incredible part is that there is a nuclear standoff between the US and the USSR due to a Ukrainian secessionist movement.
David Brin’s The Postman (1985) is about the aftermath of a nuclear war and subsequent American social and political collapse, but the enemy in the war is described as the “Slavic Resurgence” ruled by “Slavic Mysticism” rather than the USSR ruled by Communism.
This is not what the OP asks for exactly, but I think Ayn Rand’s 1957 book Atlas Shrugged does a remarkably good job of predicting the implosion of a Soviet Union-like economic system.