The invaders are flying the Soviet flag on their vehicles and wearing it on their uniforms. They are not even hiding their intentions.
During my time I saw some US soldiers flying\waving the Confederate battle flag. I never interpreted it as their intention to reestablish the Confederacy.
Russia has private business, property etc. something the USSR never allowed. It’s more an authoritarian Fascist-like state then a communist\socialist one. Emphasis on authoritarianism not internal economic policy. As a comparison, China currently is also more of an authoritarian Fascist-like state then a communist\socialist one, communist trappings aside. In fact, moving toward Nazi-like state with its growing internal emphasis on Han racial superiority. Xi is slowly encouraging a very Hitler-like (and Mao-like!) cult of personality. Its possible they may completely move back to the Maoist type of state, but not there yet.