German National Socialists, btw, didn't insist on formally owning all the means of production. They just appointed people like Fritz Todt and Albert Speer to control them.......which btw is what FDR did over here, and even went so far as to have troops throw Mr. Avery, chairman of Montgomery Ward I think it was, out of his own office, to make his point -- that everyone had to toe the mark and pull together for Victory. Stalin would have had the guy shot, but the end result was the same.
And the idea of controlling property without owning it has been voguish in the U.S. Left for a while: Barry Commoner ran for President in 1980, as you may recall, and he made that same idea his own: we'll let people continue to own property -- we'll just separate them from control, which we'll exert to turn capital to public purposes. Broadcasting that idea netted Commoner a lot of appeals from liberals to shut up -- he was letting their favorite cat out of the bag!
Whether they are outright Communists or corporatist fascists like the Nazis who permit a private sphere to continue in existence under State controls and intervention, socialists are all still parties of Government Control and are therefore leftist, IMHO.