Everyone knows, even in russia, that the war is a desaster.

And now Prigoshin and his Wagner forces, who stood for the only few victories in the last time, turned against Putin. (Even stating, that the war was wrong in the first place and that there never was a threat from Ukraine towards russia.)

And Wagner has the reputation of being ruthless and efficient.

The common national guards really don't want to fight them. They could surely bomb them all to death, but then who will fight and win for russia?

There is currently a ukraine offensive going on. And Wagner occupied an important military HQ in rostov. They will never forgive Prigoshin for that, that is sure, but he plays the only card he has - brute force.

And they came already within 250 km of moscow with little resistance. But that is also, because they don't want to actually fight.

That's the problem for these kinds of strongmen dictators - any sign of weakness is a major political problem and one which he may not outlive. And in fairness to Stalin (and you won't hear me complementing Stalin too much usually), he didn't flee Moscow in 1941 when other armies were approaching.

At this point, I think Prigozhin is more likely trying to get a deal to leave russia and keep his billions & life.

Highly doubt Wagner will be kept around and likely the defense minister will be kept. That said, the defense minister ran away in the fighting, probably justification to sack him