I wish I were currently up on my historic Kremlinology to remember how close this moment already is to the one where Khrushchev was removed from office OTL.This might be a good way Khrushchev to bring the KGB down a peg or two and get them in line.
The reasons the Politburo turned on him all related, OTL, to stuff that was already done by this point--the outcome of the "Caribbean Crisis" as they called it in Russia, being the latest and worst perhaps, but also a bunch of other fiascoes, some of which such as the disastrous outcome of the programs to intensify agriculture in Soviet Central Asia, wouldn't even have their full impact known for generations to come but already were disruptive enough.
All that said, I personally suspect the USSR might have been better off sticking with NK, though his mercurial nature was a series of international crises waiting to happen--not to mention his tendency to step on toes within the Soviet apparatchik system which is what ended his career politically. (Albeit also with the salutary but not much followed example of a mere political removal without actually killing the man--and to be sure, OTL he didn't live out another decade and presumably if he can dance his way to keeping his position, the stress of the top job can only be guessed to kill him even sooner).
So if I had to bet money I'd have to bet that he is on the way out pretty much no matter what, and we'd be lucky if the outcome is as OTL with Brezhnev being put in as the figurehead of a truly collective and somewhat collegial Politburo.
Personally I would like to see him manage to stay in power, ideally on the assumption that just as JFK (and presumably LBJ, standing near the fire though not in it) was much sobered by the Cuban Missile Crisis, so Khrushchev also learned some hard lessons about being circumspect and meticulous. Presumably if NK can manage to recover his balance (and I have to assume he didn't realize how thin the political ice he had skated onto was, so this requires some ATL insight he lacked OTL) he has to do it with the help of allies he has to reach new understandings with--that is, the Politburo will indeed become more collective and less a one-man show no matter how the dust settles, with Khrushchev becoming consciously and somewhat painfully beholden to other top dogs in the Communist leadership he must act in accord with. (Maybe this will take some of the weight of responsibility that might otherwise shorten his life off, but vice versa he surely would be frustrated to have to get everything talked out and countersigned by his supporters. Just maybe perhaps he would at any rate be sobered into setting up clear lines of succession against the day he drops dead or has a stroke or something like that).
Still the way to bet is that it is too late for him to recover his own equilibrium, even on newly restricted terms--and indeed while for a decade or so he has in fact been the de facto Number One, all along since Stalin's death the Soviet leadership has been cautious not to let that power become irrevocable and unchecked.
So, one way or another, the Kremlin itself is in a tailspin and has been before the Day In Dallas.
And while OTL's outcome was not so great for long term survival of the USSR, in the shorter run of a generation or so, it definitely stabilized things and put the USSR on a more comfortable, complacent basis than it had ever seen in its history. Arguing for a path forward for the Soviet system to avoid its final breakdown as OTL is a bit controversial to say the least and quite problematic no matter how much enthusiasm one might muster. I refuse to totally throw in that towel but admit, it is a big ask and one that needs its own TL, not a side effect of one focused elsewhere--the way to bet is that OTL outcomes are about as good as it gets actually.
Kremlinologists up to speed might have a lot to say here and now about what the crapshoot odds are for the sort out in the Kremlin now, with this ATL wild toss thrown in.
I appreciate that no TL author can definitively state that there was in fact a KGB operation, mainstream orders or "rogue," since that would be playing around in the OTL conspiracy theory sandbox; this must remain obscure and speculative.
FWIW I personally would strongly doubt the agency would dare mess around like that nor be so disorganized as to allow some gang of hotshots to play with it off the books. The general track record of the Soviet form of authoritarianism was that they were risk averse--no move so drastic would be allowed without checks to bring approval or otherwise up to the highest authorities, nor would any of these be so gung-ho as to play with this kind of fire, not with these persons having some clue as to just how devastating a US nuclear strike would be. It would be one thing if Yankee arrogance were backing the Soviet empire into an existential corner, then there might be no telling what some people might do, even on their own authority and with deniability. But given that Kennedy had clearly opted for "live and let live," that Cuba remained uninvaded, that he clearly did not want a hot war in Europe if he could avoid it, that both he and the Soviet Premier had agreed that the number of US or Soviet cities they were prepared to see go up in a nuclear fireball was in fact zero--I don't think anyone no matter how dogmatically Bolshevik or just plain bloody-minded would intend an actual assassination to go forth. They might dream of it and even speak for it rhetorically to score ideological points for bulge in Politburo deliberations--but when push came to shove, even if gaining complete control of the machinery unchecked, such persons would think twice when it came to actually ordering it. These guys had barely survived the Great Patriotic War--confident they might be that the Communist system would be the one whose remnants survived to rule the ruins of the world, but they would not estimate the odds of their personal survival to be ones to call the shots over this post-apocalyptic mess all that high. Again, if they were desperate it might be one thing, but just sticking to playing cautious chess, these fellows were in a comfortable position, why set it on fire just yet? I think the evidence is that the Kremlin had long ago evolved checks on checks and the Soviet system favored central command and control and did nothing without intending it. The highest value was keeping control, and if that blunted their effectiveness, so be it. Hotheads would be watched and reined in.
So, if a political churning up of dirty laundry were to happen in Moscow, the honest evidence turned up would probably let the security men off the hook and if anything position them for a stronger voice in governing the Soviet system going forward--which is more or less what did happen OTL, and I've seen TLs that put these gray figures even more in charge, with ugly results even versus OTL for the system as a whole.
I suspect the likeliest upshot in Russia is something substantially similar to OTL, whether NK stays in the nominal Premier position or not--if he does so, it will be with clear and openly (though privately) given agreements to defer to the collective and do nothing without their prior approval, and that while certain factions will emerge as the most important, others will not be silenced (within the silent walls of Politburo chambers; to the outside world the whole gang is in perfect agreement of course). "Democratic Centralism" per Lenin in other words, only without the public aspect of laying out the losing as well as winning arguments for general consideration by Party members. It is a path toward risk-averse sure things and playing it safe, and sticking to the line that the Soviet system must inevitably catch up to and then surpass the capitalist anarchy in terms of material production and efficiency, and prevail by simply holding out and outlasting their rivals without any grandiose Napoleonic/Trotskyite crusades--just helping out this or that bunch of do-it-yourself local revolutionaries in places like North Vietnam or Ethiopia or Afghanistan, or Cuba of course, as opportunity presents, and just helping them hold out against inevitable capitalist punishment meted out to them, no sweeping Risk campaign of world conquest beyond the infallible words of Marx assuring them the capitalists cannot stand against their own working classes in the long run.
This was the comfortable groupthink, and some persons known as relative "firebrands" or "hardliners" were basically just on one end of a spectrum pushing for more proactivity in assisting do it yourself revolutionaries and in preparing the Worker's Motherland to survive the perhaps inevitable death throes of a senile but still well armed capitalist system in final panic. No doubt at least some Soviet high officials were somewhat cynical about Marxist-Leninism and just opportunistically cloaking ruder personal ambition, but my impression is that the system did tend to cultivate a certain degree of true belief to offset the grounds for gross cynicism all of them were aware of--subscribing to the belief that Leninist victory was founded in scientific inevitability would after all soothe many a conscience and ease any worries about the system evolving toward fulfillment of the promises in good time, once this terrible generation of global class war were survived, allowing the younger generations to settle into a true worker's state. By and by.