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 On a strategic and geopolitical level, Russia lost a long time ago, and the only reason they haven't withdrawn already is that it wouldn't be survivable for Putin personally - he'd get couped the moment he showed weakness.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.