Personal belief: strategic false flag. I feel it highly unlikely they truly ever planned to "take over Russia". That is most laughable to hear some people believe this - if I'm wrong, howso? I'd like to know what others think.

IMO Putin likely wanted to move his chess pieces into position, while creating confusion.

With most of the soldiers in the war zone, around 10,000 reservists protecting the capital, and very little resistance to the Wagner convoy en route to Moscow, Prigozhin could have made things very ugly for Putin, though it's unlikely he would have captured Moscow for very long, and more than likely that his forces would ultimately have been annihilated.

The more interesting question is why Putin decided to grant him and his forces amnesty. Some suggest Prigozhin retains significant kompromat on Putin and the ruling elite, others suggest that the hero status of Wagner, portrayed in the Russian media until recently, kept him safe.

Whatever the reason for the stay of execution, Prigozhin's days are likely numbered. When he's been totally erased from the collective consciousness of mother Russia, he may just receive a visit from Mr. Novichok or Dr. Polonium.

(as someone admittedly not familiar with Russian politics) I agree his days are likely numbered.

To save face, if nothing else.