I think realistically every country in the world would be smart enough to recognize Russia as the true inheritor of all of this.
We still need to remember that Taiwan still had China's permanent seat in the UN Security Council and kept it until the 1970's by using legalese black magic fuckery.
While I don't think the exact same scenario would happen, if the government of the USSR still technically exists, the Russian Federation could still be argued as a nation seceding from the USSR in legal terms. Only after every single of the 15 republics threw off their Soviet system could OTL Russia finally have the legal carte blanche to take up on the Soviet Union's legal obligations.
Very nice analysis. Another question has suddenly popped into my mind. Do you think the USSR would adopt a new, more Turkic flag, or maintain the hammer and sickle?
It's honestly up in the air, but its possible to make more Belarus comparisons to take a stab at what could happen. Belarus is what you would call a reactionary leftist regime.
While the economic system has mostly stayed top-down socialist (with the market being allowed to fill certain economic holes and bottlenecks that the state can't), the socionational presentation of the regime has been a mix of nationalism and Soviet nostalgia.
Belarus sees its period of existence in the USSR as its glory days, like how an Italian nationalist would look back on the Roman Empire. It is a quasi-fascist regime that is nostalgic for socialism.
So the actual existent Centrasian USSR would probably still try to foment the same nostalgia for its glory days, and implement that idea in its national identity. But the glorification of its pre-Soviet past is still not out of the question.
Once the Centrasian USSR government finally accepts that the gang isn't getting back together, maybe then would it start promoting Turkestani nationalism and renaming itself to something more Turkic-oriented to preserve the cohesion of what it already has. But there is no way they're letting go of their Soviet identity, it would still be seen as their glory days.
So you might see an amalgamation of socialist realism and traditional Centrasian culture prop up in the government only starting in the 2000s when the regime has found its footing. Maybe they'll choose to have the Bukharan SSR flag instead. Or even the Basmachi flag. That I don't know. But they absolutely can't keep the socialist heraldry forever.