Absolutely zero percent chance that happens. The only outcome of this is undisguised dictatorship. The only thing we don't know yet is whether it's Wagner succeeding and installing a military junta or Putin surviving and using this as an excuse to dissolve whatever semblance of a democracy they pretended to have.

Russia has already instituted conscription and civilian terror tactics and done everything they really could do to win the war - there's no further escalation available to them except into the realm of chemical weapons or similar, which would trigger further escalation from the west. And in the long run, NATO can outspend them - Russia's only real source of aid is China, who will be demanding greater and greater concessions in return. On a strategic and geopolitical level, Russia lost a long time ago, and the only reason they haven't withdrawn already is that it wouldn't be survivable for Putin personally - he'd get couped the moment he showed weakness.

Don't get me wrong, Prigozhin is an irredeemable monster who's been at the head of some of the worst atrocities in Ukraine and who has based a lot of his appeal on his pyrrhic victory at Bakhmut (while also attacking Shoigu's failures). But if the coup succeeds, he's a monster with the political wiggle room to withdraw Russia's dick from the Ukrainian beehive by blaming all failures on Shoigu and Putin destroying the great and powerful Russian military through their corruption and incompetence and blah blah blah stab in the back blah blah western decadence blah blah blah. And he will have significant political incentive to do so, since it will clear the way for the oligarchs to start making money again as sanctions lift.

And Prigozhin and his lawless band of ex-prisoners and other violent misfits gain control of Russian nuclear weapons. There are already reports of them seizing a nuclear weapons depot. This is not a turn for the better, except insofar as it could weaken the Russians' position in Ukraine. But if Prigozhin seizes power things could get worse again for Ukraine. Prigozhin's whole schtick is that the Russian military leadership has been incompetent in managing the war. It remains to be seen whether he'd go back at it harder or back out of the whole misadventure, blaming it on Putin's military leaders.

Except currently prigozhin is saying the was in Ukraine is an illegal one (to throw shade at Putin he didn't care before) but still he is now trying to play down Ukraine not up