Some guy got in a car accident(Lewis v. United States)[1] with some Federal Reserve employee and tried to sue under the Federal Tort Claims Act, which allows the federal government to be sued for certain things, like car accidents, as they are normally subject to sovereign immunity. The judge said this didn't apply to the Federal Reserve because they aren't a federal agency. There is actually a long interesting argument in the case by the judge about why the Fed is not a federal agency. They can hire and fire employees at will, their workers are not in the civil service pension program, they get workers compensation, they receive no appropriated funds from congress, they can sue and be sued under their own name, etc.
[1] https://openjurist.org/680/f2d/1239/lewis-v-united-states