That remains to be seen? Might be that some of their warriors will take the offer to join the military, and others... might select (or be given) new leadership, and go back to Ukraine to resume their regular business there.
If this really was Prigozhin vs. MoD, then that particular issue might be a closed case. Mercenaries are what they are - they're loyal to themselves and money, not state policy. Prigozhin got them to march at Moscow, so they did; then got them to march back, safe and sound, so they did. Russian government can just say "okay, no shots fired, no hard feelings" and leave it at that; it's not like they trusted them in the first place.
Putin angle though, that's a new thing. One way of spinning today's events is that Prigozhin took a swing at the Tsar, missed, and still lived to talk about it. Leaving it at that is not safe for the Tsar.
As of right this second. I hope his affairs are in order because the writing is on the wall.
I’m not saying that was the original plan, but even just moving 20K Wagner troop as part of the deal, even with no intention of attack, would draw a significant chunk of ukraines attention.
And if the Ukrainians don’t move additional defense, then an opportunistic attack might be on the table for some exchange that would be mutually beneficial to the Russian factions.
Let me be clear, this was not meant to be a grand ruse, but that doesn’t it can’t be turned in to one after the fact in order for the opposing Russian sides to salvage their situation.
Seems like a terrible outcome for Putin. He looks really weak and presumably just lost most if not all of Wagner, who were his most effective troops. He might have Prigozhin poisoned, but that would probably cause further instability internally as it causes more of his leadership to realize he'll clearly betray anybody and his word isn't worth anything.