That's wrong then. The word "soviet" means "council".. To the extent that its etymology connects to "togetherness" it just refers to the group of people coming together to make decisions.
The "union" refers to the union of the socialist republics. You can easily have "soviets" without a union, and you can obviously have a union without soviets.
https://en.wikipedia.org/wiki/Soviet_(council)#Etymology
Much like Los Angeles, if you translate the words back to their original language they become redundant.