You did not give "Marx's definition of Socialism," you erased dialectics from his analysis of the transition from one mode of production to the next. Marx frequently referenced commodity production even remaining in lower-stage Communism, the goal is to abolish it but the presence of it alone does not disqualify a system from being Socialist. State Capitalism was a descriptor for the NEP by Lenin, and he still considered the USSR to be Socialist in that it was a transitional state towards Communism.

It's extremely condescending when you act like you know more about a subject while admitting to not studying it.