Imagine a society in which every person has exactly the same sociopolitical power as every other person; representatives and officials do not have additional power; that's a property of a truly communist society.

Aren't you sort of describing democracy, and not socialism? I'm a Communist myself and I've never heard anyone claim that every person will have the exact same sociopolitical power, reading Marx or Lenin I've never encountered anything as such. Obviously people more engaged with politics should have more political power, in the sense that contributing to politics is both a privilege and a responsibility. Organizers of a local worker council will obviously have more political power than people who choose not to participate on that.

Imagine a society in which everyone's needs are met for an extreme body of needs (say as defined by the UN Universal Declaration of Human RIghts). The only transients that exist either are in a short line to be issued a dwelling, or don't want one. Everyone is fed. Everyone has their own stuff. This isn't impossible, but is difficult as heck to reach.

It's not impossible, or even difficult to reach. 1970s USSR literally had all of this. Access to a job, to housing, to universal healthcare, to free education to the highest level, to quality urban planning and public transit, to affordable basic foodstuffs and clothes, and very cheap energy, were all available. Again, I'm talking about 1970s technology and progress in a self-sufficient country isolated from world markets, without engaging in colonialism and extraction of resources from the global south, in a country that 40 years prior had been a feudal backwater in which 80% of the population were peasants, most of them not owning any land and being essentially serfs to landlords. Cuba, today, manages to get most of this, despite being in the most comprehensive economic embargo in history. It's not remotely hard to achieve this, the main obstacle to this is western imperialism doing everything in its hand to destroy any attempt, from regime destabilization, to outright threat of nuclear war, including bombing of your country to the ground (Vietnam, Korea) or support of fascists (Chile).

As for people having their own stuff:

I wonder if there's anything in common in those countries...