"The Fed" =/= "The Feds"

While it may be outside the Federal Reserve's jurisdiction, there are many other federal agencies.

The Federal Reserve is not part of the US government. It is a private organization.

It's partly private. To say it is not part of government is also inaccurate. It is independent of several branches in many respects, but relies in the government in others, by design. For example, the chair and vice chair are appointed and confirmed. Congress has oversight of the system but does not appropriate funds to the system.

My understanding is that legally, it's not part of the government. That makes it private, with any voluntary government relationships being just that. This doesn't make what you are saying untrue, but what you are saying isn't exactly clear either.

(Thought experiment: Obviously, if one did wield influence on a central bank after winning the rights to run it from a nation, one would try to keep public perceptions as wishy-washy as possible in order to keep pockets safely lined and one's fiscal hegemony in place.)

This isn't correct. The Federal Reserve System is composed of the various Federal Reserve Banks (FRBs) and the Board of Governors of the Federal Reserve System (BOG). The FRBs are hybrid entities considered to be federal instrumentalities for some purposes but not for others. The BOG is a federal agency. The Chairman of the BOG (Janet Yellen at present) is a presidential appointee confirmed by the Senate.

One wonders what kind of appointee the president is.

I did mean the feds as in federal agencies - not the Federal Reserve.

It's not the fed you have to worry about, it is prosecutors and senators trying to make a name for themselves with unnecessary law and regulations.