You're describing Parkinson's Law, which is essentially non-political. Parkinson saw the tendency of bureaucracies to expand as universal, regardless of the nature of the government or private organization they served. (One of his most noteworthy examples was Krupp Steel; the Allied air forces had destroyed every productive asset the corporation owned, but when Allied round forces captured the corporate headquarters, they found 10,000 bureaucrats hard at work).

The Deep State is explicitly political, and quite different from the workings of Parkinson's law.