What could happen? What they want? And other questions.
We can state that they have a better view on the military situation of the Russian Federation than we have. They know better what units and forced can be alerted and moved against them.
I think most if not all mobilizable units are tied down in the conflict in Ukraine, mostly conscripts are elsewhere and they can't be placed in alert in this short notice in any meaningful number. Around Moscow they bound to have a relatively strong force, which shouldn't be all conscripts. But what this "relatively" cover, I have no idea.
TschVK Wagner moves quick. They took over in Rostov at ~8-9:00 Moscow Standard Time (5:00 UTC), and then took over Voronezh by ~10-11:00 MSK . That's 500 kms as the crow flies, wtf. With this rate they should be at St Pidorsburg right now.
Oh well.

Let's say they get Shoigu and Gerasimov. Then what?
Putin renounced them - but can they be stopped, put down before they do whatever they do?
If they coup Putin?
Prigozhin said all the state machine will work as usual, so perhaps they want to swap faces in the ranks, and internally this shouldn't mean turmoil if done quick.
But will there be any international recognition? Ukraine and the West surely welcome a new regime that's willing to finish an leave everything behind. But would Prihozhin's regime do that? And if not and continue the war, would it have the relationship with other important factors like China, Iran, or India? And even if willing to make peace on the terms of Ukraine and the West would they took it seriously?
It could be a wise move to leave Putin as President, for it will allow legitimization - he is an elected leader of the RF. But could they pull this after the renouncement?

This will be very interesting to see. If the whole thing is not a scam, a media hack.