I think It's a mutually beneficial relationship. The state can hurt the billionaires, and they can hurt the state. Both of these come at a cost to oneself, so they prefer cooperating for their class interest.
I guess I don't think you are totally incorrect but this is a bad analysis regardless. You're painting this as if it was a totally reciprocal and symmetric situation. The US state is totally subservient to the billionaire class: this is evident in its financial policy, foreign policy, down to the way elections are run. The actions you may point to as counterexamples are either capitalist infighting (e.g. the tech capitalists cannibalizing media, monopolization) or the state pushing one capitalist in line to protect the collective interests of all the others. In any long term frame, the US state does nothing but protect its capitalists. That's what the state exists to do.
Like Chinese billionaires do with their party partners. It's only the ones who cause too much of a ruckus due to greed that get cut down. The others are coddled, like every other capitalist project.
These 2 sentences are an error that can only be made by missing the forest for the trees as you did in the beginning of your reply. Do you really think the PRC operates with the same guiding principles and historical outlook as the imperialist US state? Looking at the news must be very confusing for you!
Also, you reject Cuban socialism? Do you think socialism is supposed to exist in the real world or is it just for intellectual masturbation?