First question I have for you is, by puppet states do you mean the other soviet republics contained in the USSR? (Estonia, Latvia, Ukraine, Poland, there were. 15 in total)

because if so, there were essential part of the Soviet Union and had "autonomy" within their boundaries. This distinction gets confused in modern teaching and history as the USSR was Russia; however, like mentioned above it was 15 soviet republic. Think of them as states or provinces within a larger central government. And it kinda remain this way, although the fear of Stalin oppression is now gone government becomes more persuadable and people hold office longer than before. So from Stalin's until the fall of the USSR states had presidents and other officials within borders, but didn't necessarily hold much power. I believe Russian politics would like the clout (prestige) of the Soviet Union back along with the territory, but I believe common rhetoric displays that they do not want a communist government back.

Tracing this notion to modern days Vladamir Putin was recounted saying "Anyone who doesn't regret the passing of the Soviet Union has no heart. Anyone who wants it restored has no brains." This can be seen from his generation as a understanding the value of democracy, but missing the glory that Russia once held. After the collapse Russia personally took on everything politically form the USSR (crimes, debt, etc). Therefore most Russian people and the government aren't too worried about their other soviet republics. To be completely honest after WW2 there was a string of general secretaries who could not posses the same power that Stalin once had leading to a decline of power, then towards th end of USSR many of the people in power were simply too old and sick to really be a force in politics of civilian lives. Leading to a cataclysm of economic stress and civil unrest with the communistic system. By the time Mikhail Gorbachev is in power he both tries to save, but ultimately ends up collapsing the system (well in power when it collapses) due to mass reforms and changes.

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If you are referencing other territories and nations as puppet states, please say which ones and I can answer about those as well. also if you have any other questions about the USSR feel free to ask as well.