I think the issue there is article I, unlike article II, expressly states what the legislative branch consists of. And it states it consists of the house and the senate. Nothing else.
So the reading of a bank that excecutes the law establishing it, I don't know how it could fall under anything but article ii. From your explanation, that wouldn't violate McCulloch v. Maryland authorization of the executive to execute the law.
Oh, I see what you’re saying. Article I, II, and III, create “Congress,” the “President,” and the “Supreme Court.” Those are the constitutional organs of the government, and are invested with the legislative, executive, and judicial powers, respectively.
The constitution assumes you can create various offices and departments associated with each of these organs, without spelling it out. But nothing turns on where anything “sits.” The question is whether any entity is exercising the “executive power,” or “legislative power,” or “judicial power.” For example, one of the first things Congress did in 1789 was to create the Marshall’s Service to provide security to courts. These were actually created as a body in the judicial branch. https://en.wikipedia.org/wiki/United_States_Marshals_Service. But they don’t exercise the “judicial power.” They exercise executive power—law enforcement.
So the Fed “sits” in the executive branch. But that doesn’t necessarily mean it exercises the “executive power” within the meaning of Article I, Section 1.
Wikipedia link provided says Marshalls are part of the DoJ, which is the executive branch.
>The constitution assumes you can create various offices and departments associated with each of these organ
Definitely a valid point. But the legislative is unique in that the constitution explicitly defines what can exercise the legislative power, and it's defined as consisting of the house and senate. The executive and judiciary has no such restriction.