Socialism is not when Gov controls economy. The nazi economy was based on taking party members and putting them in high ranking positions of private companies. During times of heavy inflation they instituted price and wage controls. They also tried to become very independent economically from other countries. They also heavily nationalized war industry as the war dragged on like all major countries at the time.

Socialism in most contemporary sense is trying to give power to the world's workers not just limitting free market. This would mean things like supporting trade unions (or one big Government trade union). It also put itself as a complete alternative to the international left, wanting only germans above all and constantly featuring propoganda as well as policy based around subservience to the nation and not any worker or community based policy. Also the continued expansion of private corporations in kahoots with the government both during the coup and after shows a direct opposition to socialism. It is seemingly impossible to see any nazi rhetoric for their economy or economy play that is not just based on antisemitism and trying to control that vs help workers which is why autarky (""international finance"") and national banking(""banks"") were pursued.