We've seen Bhadrakumar's take on events - not a psyop, but also not evidence that the Russian state is made out of rotten wood and all Ukraine needs to do is give one final kick. Big Serge's is similar; in a paragraph:

I found the idea that Russia faced civil war or state collapse to be bizarre in the extreme and completely unfounded, but I also did not think (and I feel that events have vindicated this view) that Prigozhin was acting in collaboration with the Russian state to create a charade. If indeed the Wagner uprising was a Psyop (Psychological Operation) to trick NATO, it was an extremely elaborate and convoluted one which hasn’t yet shown any clear benefits (more on this in a moment).

I've written up a "summary" here:

He remarks about how, rather than a story being created out of the facts, instead facts are bolted on to pre-conceived stories. Everybody can pick out different details, take maybe 4 or 5 of these, and weave them into a broad and maybe even convincing narrative while not even acknowledging that alternative models could be fit to the same reality. Those who believed that the Russian state was weak saw events as proof of Russia's weakness; those who believed that the Russian state was strong saw events as proof of Russia's expert skill in creating believable psyops; and both sides accused each other of cope for it. Prigozhin was not an independent actor, he was a cog in their machine: either in Fukuyama's end-of-history machine where the neoliberal flag would be raised over Moscow as it is destined to do because neoliberalism is the endstage; or in Russia's hypercompetent psyop machine where he is a puppet on strings pulled by Putin himself. Big Serge believes that he was, indeed, an independent actor.

The mutiny was genuine but not an existential threat to the Russian state. It did indeed cause problems and may continue to do so, but these problems were and can be overcome.

While some of the confusion around events was obviously just going to happen anyway, a substantial amount was generated by pro-Ukrainian figures who were spreading rumors about how politicians were defecting to Prigozhin's side and Russian forces were, rather than blocking Wagner's convoy, joining them on their drive to Moscow. None of this happened. There are no known cases of single Russian soldier defecting, nor of any politicians or officials.

He firmly discounts the theory by the West that Prigozhin was about to crown himself Tsar Eugene the First given that, well, he was not, he never said he was going to do so, the Wagner convoy was stopped (albeit by negotiations rather than missiles), and the contagion of the coup did not spread. The next level down is "Well, okay, it didn't work THIS time, but oh boy, just wait for another armed group to march on Moscow that's more serious, or for Ukraine to break through the Belgorod front!" but unless they have Russian-supplied equipment (most importantly air defense), or all the oligarchs band together to make a palace coup, it's a little difficult to imagine anything similar happening.

He also discounts the Psyop theory, though cannot entirely (it's a theory that's kinda unfalsifiable), and looks at the following five reasons given by the Psyop group as to why it might have been done:

1. The coup was bait to draw out anti-Russian elements lying in wait to help cause a real coup. The problem with this theory is that up until this point, Putin has taken great - some would even say extraordinary - efforts to keep the war inside Ukraine. He has not conscripted anybody, there is no rationing, there has been barely any martial law (only in the four new oblasts AFAIK), there has been almost a surprising lack of restrictions on movement given the sheer number of Ukrainians that fled into Russia as refugees. It doesn't make sense that he would suddenly authorize a fake coup and break this relatively peaceful environment he has created inside Russia. But maybe he's SO crafty and SO devious that EVERYTHING leading up to this point has been an act to make those undercover actors THINK that he would never authorize a fake coup - and sure, okay, but it still failed to actually draw out those undercover actors. But maybe it DID and we just don't know about it! Okay, sure, but then it's unfalsifiable.

2. The coup was designed to create a massive scene of chaos to mask troop and equipment moving around to the fronts; Prigozhin's permanent vacation to Belarus added fuel to this fire. The problem is a lack of understanding of how military forces are set up. You cannot just drive a hundred tanks into position overnight and then start driving and firing forward. You need to set up supply lines, get the ammunition warehouses prepped, get the fuel prepped, build infrastructure. But let's say that the Russian state is so good that this actually is enough time - the question then is, sure, you can fool the media and the commentariat, but can you fool a bunch of satellites and informants living close to the border, even if everything's moving around all at once? Probably not. Additionally, Prigozhin might not even be followed by Wagner anyway. And lastly, every day that goes by without a Russian attack suggests it wasn't for that purpose. "But maybe it WAS for that purpose but the Russians figured out it failed to fool them and so didn't attempt it!" Again, unfalsifiable.

3. The coup was designed to give Putin the mandate to amp up the war and move from an SMO to a Counter Terrorist Operation (CTO) or even outright war. This one is only really peddled by dipshits. If the Belgorod attacks and the drone attack on the Kremlin aren't enough reason to do so, then this sure isn't. And, again, Putin has taken great pains to keep the war and its effects inside Ukraine.

4. The coup was designed to oust Shoigu and Gerasimov, who Putin secretly does not like. Why on god's green earth would you remove two very high-up officials in your government by doing so while bowing down to a coup plotter? This is literally the worst way you could possibly do it - it makes Prigozhin the kingmaker and not himself. Also, Putin likely does not hate Shoigu and Gerasimov (and I, like Big Serge, think the claims that these two men are incompetent are at best an exaggeration and at worst, absurd to the point of revealing that you don't understand how complicated wars are, especially when you're up against the entire West).

5. The coup was designed essentially as a fire drill for a real coup, to see if the Russian state could handle it and if it couldn't improve or eliminate weak links. If it was, then everybody passed with flying colors, complete with one Russian governor urging Prigozhin to, well, let's say 'take a long walk off a short pier'. Why would this fire drill need to be done at all? There's been no signs of internal dissent, certainly less than in Ukraine (or even, for that matter, several western countries). Even the Communist Party has always been behind Putin. There's also been no big embarrassing events lately that could be making officials have second thoughts. Bakhmut is captured and the counteroffensive has, so far at least, failed. Belgorod is a touchy subject but it's not actually dire.

Near the end, Big Serge talks about Wagner and Prigozhin and what his motivations were, and concludes that ultimately Prigozhin was a man who was taking a big gamble despite not having a winning hand (I don't know how poker works so just insert an analogy here) and Putin called his bluff. In his wildest dreams, he might have imagined a country firmly on his side and not Putin's, with the same kind of late-Soviet bureaucracy that made decisive decisions near-impossible to enact against him, and most importantly some sections of the military willing to give his soldiers food and equipment and ammo. He may have committed the cardinal sin of believing his own propaganda about the Russian MoD. In reality, he got none of that and is now walking with his tail tucked between his legs to Belarus.

And finally at the end, he discusses the often-made analogy of this coup to 1917, and says that they aren't just not the same thing, and they aren't just not even approximations of the same thing, but they were actually opposite things.