I may be mistaken here, but I’m pretty certain people still got paid money and could do what they liked with it.

Like everywhere else. There were limits on what could be a private property, but there was stilll a private property. West calls USSR "communist", but according to communist party people were still building communism, not living in it. IIRC the term used right before the collapse was "mature socialism". Now when I think of it, I do not remember a deadline for that building to finish ever being mentioned.

Dunno about Soviet Union but in communist Poland there were national banks and they managed saving accounts for workers. It was optional but heavily encouraged, part of your earnings went directly to it every month. It was called "PKO Saving's book".

My grandparents participated in it and after decades of saving a few percent of their earnings each month the total from both of them was just enough to buy their grandkids 2 pairs of shoes :)