Isn't it just Prigozhin who's going to Belarus, and not the entire Wagner group? From what I understand, some Wagnerites will be integrated into the regular army, while the rest return to their old positions.
Anyway, I doubt that a second attack from Belarus is ever happening at this point. The first rush to Kiev/Kyiv/whatever failed despite them having much bigger numbers than they could have now, as well as the moment of surprise. Now, the border areas are mined and completely covered by pre-sighted artillery. Unless the Russians, for some reason, decide to repeat the Vuhledar fiasco, there's nothing of the sort happening.
At this point, just about the only move for Russia is to strengthen the defenses in Zaporizhzhia and throw everything and anything possible there to make absolutely sure that Ukies will never be able to cut the land bridge to Crimea in two, because the moment that happens, it's pretty much game over.
Nothing will happen probably. War will continue. Russia will eventually lose and blame the ministry of defense completely. Pull out and continue to rot.
Let's also not forget that just before this whole thing started, Prigozhin was, as usual,
ranting about the war going much worse for them then the military commanders were telling Putin and the rest of the world. He even mentioned that there's Ukrainian forces near Tokmak already, which is one of the main railway hubs in the area, and, coincidentally, some maps are already showing "partisan activity" near the city, when the AFU should still be dozens of kilometres away
. If a logistics hub like that gets retaken, well...