I'm not sure what Prigozhin's chances of successfully pulling off a coup are (nonzero?), but Russia has been heading for an unambiguous military loss for a while already and now is looking at a complete military disaster (loss of Crimea is on the table), even if Putin manages to bring Wagner under control. I don't see how this is politically survivable. What's the spin? "Ok, I sacrificed tens of thousands of Russians on a catastrophic invasion, but at least I managed to stop a coup from my career-criminal personal cook (whom I also outsourced a good part of the war effort under his blatantly unconstitutional private military outfit to)."?
I have long thought the West should be a lot more scared about what it's going to look like if the country with the world's largest nuclear arsenal becomes completely destabilized. Seems like we're going to find out.