Except that with the USSR falling the transition of power for Russia was a bit more peaceful

At the time that wasn’t a given. Gorbachev was under a lot of pressure from hardline communists within the party to crack down on the uprising and no-one really knew where the loyalties of the military lay. As it turned out Yeltsin won the day and the transition went peacefully but it could very easily have turned out differently.

Just to add to this, a Prigozhin government would likely be far worse for Ukraine. While Putin had few qualms brutalizing civilians and committing war crimes Prigozhin has none. He’s a ruthless, murderous thug. The best outcome would be that he is defeated by the Russian military but that they have to withdraw troops from Ukraine, allowing the Ukrainians to seize the initiative with their offensive. The worst outcomes don’t bear thinking about.