What happened in the Soviet Union is more complex than that. I want to emphasize that I don't support the majority of actions of the Soviet government and virtually none of the Stalin government in particular, but it is important to understand how society got where they were.

First and foremost, it is wrong to think that absolute power in a few people is absolutely necessary in this system to work. The reason that the Soviet Union fell into an authoritarian dictatorship is a result of their attempt at rectifying the old system. A strong believe specifically in Marxist-Leninism is that the only way society can move onto true and free socialism is if first, the bourgeoisie is completely and utterly removed from existence. They believe that if anyone still has a semblance of capital based superiority, that capitalism will always have a ground on which it will rise again, no matter how good their society might become. This lead to the believe that, "for now", society needs to be led with an iron fist by idealists who know what's good for it. This obviously fails once anyone with the will to abuse this system gets into a position of such power. There was no plan to get rid of them, no clear mechanism that would enforce their path towards the dissolution of this authoritarian state as was promised and finally no way out of it.

Socialism doesn't need to mean that an authoritarian government owns everything forever. If that were the case, you'd effectively be no better than under capitalism, as all that has happened is that an elite above the worker class has taken control and the worker class is forced to accept it's role in their plan. Even in the Soviet Union, one of the most famous planned economies in history, it was meant to be a temporary state just to set up a stable system and then transfer it into local worker ownership.

What has been shown to work well is at the very least the concept of a cooperative ownership where the workers own companies collectively and benefit from the profits together. While they aren't incredibly widespread, they exist even in countries like the US. Most of them are found in the agricultural sector, but you even have examples of more widespread application of the concept in companies like Mondragon in the Basque region of Spain.

The specifics of where these should ultimately go would completely blow up this conversation and there are better people you can talk about it with than me (just don't try it on hexbear), but the point, in short, is that no, Socialism doesn't imply any of those points you mentioned, but yes, attempts and supposed attempts to instate it have ended in system supporting these things. That doesn't mean that they are intrinsic to Socialism though. There are many factors that play into why it has historically failed and it serves to note that a major part that has made the development of a socialist society near-impossible, even in a good willed system, is the extreme pushback this has received from countries that were capitalist and where the elite was afraid of losing their advantage.