Nah, if Prigozhin doesn't have loyalists installed at FSB, Interior, and Defence he's a dead man. I guarantee you he knows this. You don't get into a position of power in Russia without knowing that. His lead elements were holding an Operational Rally Point just outside of Moscow when they just... turned around and a promise...? From Putin...?

No chance, Prigozhin may be a ruthless, cutthroat sociopath but he's not an idiot. Add to that Putin called him out as a terrorist, a mutineers, an enemy of the state, for Putin to U-turn makes him look weak. Sure, the leverage is there but there's no way you make him look weak and just walkway... not AND survive for very long...

Yeah, He has to have his people installed at Defence, FSB and Interior, and at that point he's in charge of the Russian Federation in all but name.