One of the primary features of fascism is government control of private property for the common good, as defined by the state.
Fascist Germany had a veneer of capitalism on the surface, but underneath thousands of fascist functionaries controlled the businesses through bureaucratic dictates.
Hitler stated several times that private property was allowed provided you used that property to carry out the will of the state. He realized that his followers were idiots and could never be expected to manage industry, supply and distribution.
Businesses, in turn, had great difficulty in managing their day-to-day affairs, as dicates coming from the state could change from one week to the next. Many businessmen took to studying Marxism to try to understand what the state wanted.
It’s documented in the 1939 book titled “The Vampire Economy.”
Actually, Germany wasn't "fascist". There are doctrinal differences that were of no interest to Americans fighting both Italian fascists and German Nazis, but German and Italian political literati understood them well.
As you say, the State is paramount in fascism, and in a fascist system all persons, capital, and activities exist to support and carry out the will and the best interests of the State. A consequence of fascist thought was that the old nobility were tolerated because their prestige and social authority, if propery used, served to support the State. Nazism, however, did not promote and sustain the old family pretensions. Neither did Communism, which waged class warfare on them.
National Socialism is a species of social-ism, and as in Communism the interests of the People are (theoretically) paramount -- das Volk. Nazi theorists and mountebank scholars of the SS-Ahnenerben spent a lot of time glorifying the misty past of the German Volk and connecting to it, to uphold their political claim to be defenders, champions, and agents of the German People in just the same way that the Dictatorship of the Proletariat was claimed by Communists to be the shield of the working class people.
The Russian Communists likewise wore out the Russian word narodny, "of the People", in providing names for their institutions and government organs: The People's Bank of Moscow, for instance, is today known to us simply as Narodny Bank.
It’s ironic, isn’t it? They defend abortion as a “right to privacy” but we don’t have the “right to privacy” for our own money.
Of course, they don’t base their ideology on logic anyway. It’s based on their utterly selfish bestial desires. This is a brave new world. Even my own father, who is supposed to be my mentor, is utterly mesmerized by socialist lies. I can’t escape the horror of it all.