The Russian military brass told Prigozhin that his independent Wagner group would be incorporated into the Russian military as of July 1 and be subject to the chain of command. Prigozhin and his commanders rejected this and saw it as an act of envy of the Wagner Group's success compared to Russian Army units.  The alleged "march on Moscow" was a protest to get Putin's attention, not an attempt to overthrow Putin or the government.

On June 29 Putin met with Prigozhin and his commanders for several hours where the Wagner commanders gave their version of events and expressed their commitment to MotherRussia.  Having witnessed the Wagner Group's effectiveness in battle, Putin was desirous of keeping the Wagner Group on the front line in Ukraine.  The Belarus president, Lukashenko, also wanted the unit and invited them to Belarus.  

Prigozhin and his commanders agreed to be incorporated into the Russian chain of command.  There is no information whether Putin met Prigozhin's demand/request for a more competent Russian general staff and a more determined effort to bring the conflict to a victorious conclusion.  

Clearly, no move has been made against Prigozhin.  He is a billionaire Russian businessman separate from his Wagner Group, and no moves have been made against his business.