But the fact is they didn't nationalise the vast majority of German industry. To claim that they did is just ignorance.
Most German private companies remained private companied. They were owned by private individuals, shareholders etc. They employed people who they paid wages to, and made profits or losses. This is capitalism, whether under a relatively "free" democratic electoral system or a one-party state. It's not socialism, in any accepted understanding of the word.
The Nazis used their one-party authoritarian power to increase the role of the state in their mixed economy in certain specific ways (linked to their fascist ideology), like protecting German industry from imports, prioritising German citizen workers over immigrants, increasing production for the war effort etc. Some of this was not particularly different from the state-mandated production increases, imposition of rationing etc. that took place in Britain and other countries during the war. Wars tend to move countries toward increased centralisation of economic decision-making, regardless of their underlying economic system.
But they didn't nationalise that basic underlying system (in the way that Mao or Lenin did, or you could argue British Labour socialists in 1945 or French socialists at various times started doing and would have completed if they hadn't been voted out first). They just didn't.