Or maybe he told Prigozhin he'd back his coup attempt, so Prigozhin would make the first move and look like the instigator, so Putin and the MoD could look like they have the moral high ground by "defending" Russia from Wagner's "unprovoked" coup.

It's exactly the kind of "seems clever until you think it through for longer than a few seconds and realize it's absolute idiocy" type shit Putin pulls all the time.