I am only postulating
From what I have read it doesn't seem Pugachev had any motive for a modern pluralistic and popularly lead government but rather an affirmation of strictly Russian Tsarist rule (Peter III or otherwise

) over a feudal domain as denoted by his overtures to make Cossacks and the like land owners. As much as they new government will ease the burden of the peasants and the rest of the country I can't see an ultimately decentralized government as this being able to undertake carving out Novorossiya, Crimea and conquering the Caucuses as quickly. It could also create an opportunity for a free Polish state. This would also butterfly Russian holdings in North America that ultimately wound up with the US much later. Another glaring fact is this Russia would certainly be kicked out of the club of European monarchs.
I could even go as far as seeing Catherine and her government fleeing to establish a realm in exile in Kiev. Who are certainly filled with those more interested in maintaining trade with Europe then remaining a part of an ever isolated Russia.
