> It is funded by profits of their actions like a private entity.
The USPS is an independent agency of the federal government receiving no taxpayer funding (except for services like postage purchased by other government agencies) that is funded by its own operational revenues.
The parts of the Fed that aren't the Board of Governors aren't really like that, either, though.
> an independent central bank because its monetary policy decisions do not have to be approved by the President or anyone else in the executive or legislative branches of government, it does not receive funding appropriated by Congress, and the terms of the members of the board of governors span multiple presidential and congressional terms.
The first and third are the typical things that define “independent” federal agencies, the second is true of some of them (e.g., USPS).
The structure and composition of the Fed is special though, even in that context, but “private” seems to be misleading behind a false dichotomy.
It is kind of (though this term is charged because of the role corporatism played in the fascist public ideology, though the term is much older and not generally associated with authoritarianism), something of a corporatist institution in and by which state and private power are aligned.