chapotraphouse

The phrase was originally coined to refer to all the career bureaucrats and functionaries that persist through administration after administration due to being "apolitical", actually materially enacting policies or serving as consultants and sources of information for formal leaders. So yes, that is literally what the "deep state" is and what it meant before it got appropriated and warped by weirdo reactionaries who needed a new word for "illuminati" after that got too commonly recognized as nonsense.