Right now we are all guessing, aren't we?
I doubt the Wagner group members that are now back at the front against Ukraine will stay there very long.
They are mercenaries and loyal to whoever pays them. Those of them who are Russian citizens presumably know precisely what Putin's statement that they will not be punished is worth and will leave as soon as they can via Belarus.
And no-one on either France 24 or Deutsche Welle has suggested that Progozhin is out of the game. Presumably, he has lived to make all the criticisms of Putin, Sjoigu and Garasimov that he has made, plus got Putin to rescind the statement that everyone who had taken part in the revolt would be punished to the extreme of the law (and we Russia-watchers know what that means) because he is holding a very powerful threat over Putin. Otherwise someone would have shot him in Rostov on the Don the other day. If not long before!
Whether Progozhin will withdraw the entire Wagner group from Ukraine and hot-foot it to the Sudan or Syria, or anywhere else where he can earn money fighting, or not, I certainly cannot say, but I doubt he will suddenly leave his men to fend for themselves.
I hold no brief for Progozhin, but give the Devil his due! like any good captain of mercenaries from the middle ages to today, he has never before left his men to fend for themselves, so I doubt they have been so left now. Nor do I believe for a second that they will sign contracts with the Russian defence ministry.
It would not surpise me if it turns out that Progozhin has done exactly what he had planned to - he has exposed the fact that either Russia has no troops at home to defend Moscow, or that the army, military intelligence, the FSB and anyone else you can think of are all so divided in those who still support Putin and those who want rid of him that it actually was possible to get as far as he did with no attempts made to stop him, or none made by people who actually knew what they were doing.
Putin now has to spend time assessing whom he can trust and whom he most assuredly cannot trust, get rid of those he deems unreliable, find a scapegoat or two etc. etc. Expect Stalinist purges and a series of tranparent lies.
I have been waiting for a revolt ever since Speznav and the 94th Artillery refused to fight in March of 2022.
Progohzin has clearly told any former members of the USSR who are unhappy with the way Russia is treating them, "Come along, chaps, march into Russia no-one will or can stop you! "
You know someone might just do precisely that.