Prigozhin is not looking to be the next leader of Russia at all. He is a Talleyrand/Richelieu figure, he is perfectly happy being in the backline and he isn't really liked enough by any faction of the Russian elite either. He also really is not electable at all given his past.

That said whatever happens Prigozhin's rep has been steadily increasing this SMO, given Wagner's performance relative to the regular army.