You are trying to slice up parts of a cohesive system and treat those constituent parts as though they form an independent system themselves, but this is incorrect.

Ah, I see the issue here. I am not arguing that the system is entirely capitalist or socialist. I am arguing that a system can contain sectors that operate under one system while other sectors operate under the other. The “principal aspect” certainly applies as a general description of the whole, but that doesn’t change the nature of individual elements.

Classes are relations to ownership of production and distribution, not simply income levels or levels of administrative authority

I would argue classes are determined by power. In the USSR, the power was held by the government and organized crime, not workers.

The US is a democratic republic. No matter how much capital you have, you can’t gain power without convincing people to vote for you. Granted money makes this easier, but it is not sure thing. Look at Elon Musk. He tried to use his money to force his way into government with that DOGE thing, but it failed miserably and he was pushed back.

The majority does not run society, they pick between outcomes already decided as okay by the capitalist class.

Was it any different in the USSR with the party making all the choices? Power always sets up the game board we all play on.