The US Attorneys are not vested with independent power as a fourth branch of government, in the Constitution.
Prosecutorial authority is vested in them directly, not through the Attorney General. Like the Supreme Court and the US Attorneys, The Attorney Generals office was also created in the Constitution, and established in the Judiciary Act of 1789, but not in a supervisory, or chain of command role over the US Attorneys. The Department of Justice was established much later.
The US Attorneys are part of the Executive Branch and have always reported to the president, first directly, then indirectly through the Department of Treasurey and then indirectly up the DOJ chain. They currently report directly to the DAG.
They are part of the Executive Branch. They are not independent, nor philosophically should they ever be.
“The US Attorneys are directly vested with power in the Constitution.”
“The US Attorneys are not vested with independent power as a fourth branch of government”
They are not a fourth branch of Government, but they are vested with independent power.
The President does not personally have legal arrest powers, but he supervises and commands others who do. The President does not have the legal power to issue a subpoena, or convene Grand Juries to bring serious charges before a court. US Attorneys do - directly.
The President can nominate or fire US Attorneys. The Attorney General can issue all kinds of directives and guidance, and add or subtract budget and personnel positions. But nobody has legal authority to order a US Attorney not to prosecute a crime, if that US Attorney does not agree with the rationale.