Late Stage Capitalism

Socialism does not necessitate the abolishment of commodity production in totality to be considered Socialist, just that the society we are analyzing is working towards abolishing it in the future, which is further cemented by running an economy where the overwhelming majority of large firms and key industries are in the public sector and thus have leverage over the rest of the economy.

This is because no system is static. Whoever controls the Means of Production controls their development, and in which direction. As production improves, centralization increases, and state management becomes more feasible and more fundamentally necessary. This propels further socialization of the economy, as long as there is a dictatorship of the proletariat, the development of the productive forces drives the development to higher and more developed stages of Socialism, eventually giving way to the establishment of Communism.

Further, to compare China to fascist Mussolini is just absurd. Mussolini had minor nationalizations, in order to support the Capitalist state. In China, it's fundamentally the opposite. Engels went over the difference in Socialism: Utopian and Scientific:

But the modern state, too, is only the organization with which bourgeois society provides itself in order to maintain the general external conditions of the capitalist mode of production against encroachments either by the workers or by individual capitalists. The modern state, whatever its form, is an essentially capitalist machine, the state of the capitalists, the ideal aggregate capitalist. The more productive forces it takes over into its possession, the more it becomes a real aggregate capitalist, the more citizens it exploits. The workers remain wage-workers, proletarians. The capitalist relationship is not abolished, rather it is pushed to the limit. But at this limit it changes into its opposite. State ownership of the productive forces is not the solution of the conflict, but it contains within itself the formal means, the handle to the solution.

Engels is specifically speaking about economies where the state is thoroughly bourgeois, and thus the character of the state ownership is to support Capitalism. This is not the case for China, however, which has gradually been seeing large gains for the working class and the Capitalists within China thoroughly submissive to the proletarian state. China has already had its revolution, it did not abandon it, neither did Cuba, Vietnam, etc. This is supported by what Engels says later:

The first act in which the state really comes forward as the representative of the whole of society -- the taking possession of the means of production in the name of society -- is at the same time its last independent act as a state. The interference of the state power in social relations becomes superfluous in one sphere after another, and then dies away of itself. The government of persons is replaced by the administration of things and the direction of the processes of production. The state is not "abolished", it withers away. It is by this that one must evaluate the phrase "a free people's state" with respect both to its temporary agitational justification and to its ultimate scientific inadequacy, and it is by this that we must also evaluate the demand of the so-called anarchists that the state should be abolished overnight.

Production is gradually transformed into public property as it develops and is more capable of being publicly owned and planned.

But you've already been explained this before, repeatedly. Your stance is that there can be no such thing as Socialism until commodity production, markets, and money all cease to exist, when in all likelihood vestigial elements of each may continue to exist even in the earliest stages of Communism, if we agree with Marx. Your stance is the "One Drop Rule," which eliminates the entirety of Dialectics and treats Socialism as a unique mode of production defined by purity, while Capitalism, Feudalism, and so forth were all defined by which element was the principle aspect, as no system has ever truly been "pure." This is plainly a wrong stance to take.