If this goes on long enough it will most likely fuck up morale and put a considerable strain on the actual state army. That might give Ukraine time to at the very least recover. If the internal devastation is big enough whoever comes on as the next dictator might even have to technically end "the special operation" because there's no resources to keep it going and they could do so while saving face, because it's technically Putin and Shoigu's fault for mismanaging everything. The totally best possible scenario is this happens, it takes them a few years to build the military back up and meanwhile Ukraine manages to get both in the EU and NATO, at which point attacking them again becomes a whole different deal.

That's most likely a terribly unreasonably optimistic scenario. More likely whatever it is that's happening right now takes a few days, either Putin or Prigozhin dies and things keep on going somewhat the same, regardless of who's the de facto dictator. The country is mostly being ran by shady business interests that depend on the dictator, but if they agree on installing a new one could do it.