Whatever you think about elite politicians and the super-rich, they’re not the “deep state”.
The whole idea of the deep state is that it’s part of the state, ie government, so not private citizens, and they’re “deep” ie hidden below the layers of government. Thats the exact opposite of politicians and the ultra rich.
Lol I'm pretty sure the "deep state" just means, "manipulating the levers of power from a place without accountablity/oversight" which covers both these shadowy hidden layers of govt you describe and the shadowy wealthy elites funding and lobbying for whatever. It can be both.