I: The Object-Level Scholarly Debate
One of the oldest questions of constitutional law is whether, and to what extent, the President has the power to remove other executive branch officials; as well as whether, and to what extent, Congress has the power to regulate or restrict any such power. It dates back to congressional debates in 1789, the impeachment debates of Andrew Johnson, and Supreme Court cases from Myers v. United States, to Humphrey's Executor v. United States, to Seila Law v. CFPB.
Another one of the oldest questions of constitutional law is whether, and to what extent, the Constitution's vesting of "the executive Power" in "a President of the United States of America" includes various powers not specifically enumerated elsewhere in Article II. The two questions are different, but they overlap, because one of the strongest arguments for an executive removal power is the argument that appointment and removal of executive officers was understood as an executive power even without being specifically enumerated.