You are correct on what state capitalism is, but that flies in the face of the cases discussed. Perestroika USSR is not Lenin's USSR, but one that suffered from decades of revisionist rot that started before Stalin's corpse was even cold.

Normal-ass private citizen capitalists are anathema to Lenin's state capitalist model, the whole point was for the state to take that mantle in order to remove the existence of an independent capitalist class. I don't think this was correct, and in fact a pretty catastrophic failure of grasping counterfactual class antagonism, but it is what it is.

China's model is officially called (among other things) "state socialism", so named because the primary role of the state is not to nullify and supplant the capitalist class but rather to subjugate it at the direction of the proletariat. We can say in a looser sense that things like it's public enterprise in oil are "state capitalist", but the PRC overall is not a state capitalist entity.