So my current take on the MoD and Wagner situation (Which is what I will refer to this 'coup' as) is that Prigozhin is holding Rostov rather peacefully all things considered over his beef with the big boys in the Russian MoD. RFA/Nat Guard have been activated, but no real fighting. The FSB isn't doing anything drastic outside of pulling out of offices. So there's no substantive fighting. Moscow looks to just be being secured in a typical 'Just in Case' type of situation
Cont:
It appears that Prigozhin's actions have been over long known criticisms of Shoigu and Gerasimov running the war poorly. In so far as they have to lie about numbers, success, and handling the front half of the war while Wagner is the only group really capturing success in offensives. He has not criticized Putin, nor his regime. His words and actions seem to be directed at the MoD, and IF anything were to happen from the actions of Russian Military Apparatuses suggest they won't intervene
Cont 2:
So essentially the Russian State and Putin will be left aside to let this happen/take a side as of yet. Does not seem overtly violent as of this posting.
Largely a protest by competent military command against incompetent superiors. Who is to say what caused this, but so far from my looking at this is all that can for sure be corroborated based on current actions, and direct video evidence.