Yes, everyone had a job. It was illegal not to have one. Jobs were basically assigned by the state. Most “normal” people could choose among a few OK-ish options. But if you got a hair out of line or crossed wrong people you could get assigned shoveling coal in a small boiler room or building railroads in Siberia. And if you didn’t want that job you became a criminal and went to some mine or quarry working double shifts for gruel in Gulag.
Yes, everyone had a roof over their head. But that doesn’t mean space, comfort, or even privacy. It wasn’t uncommon to have no more than a bed and a small cabinet or chest. Most of the living spaces and urban areas were extremely depressing. It’s all grey boxes and muddy trails. The best you could hope for in most places is some trees and bushes adding a bit of green in the summer.
There was very little people could do to change any of that. You couldn’t move elsewhere just because you wanted. People in cities with better professions could move if they managed to know the right people and could get a job elsewhere. People in villages were basically pinned to their colhozes. Their only option to see other places were a holiday trip if the managed to save up a little or to go into military and be stationed wherever.
This lack of agency resulted in mass depression and alcoholism.
Where do you think the grim and drunk russian stereotype comes from? It’s just the soviet reality.