I think Myers v. United States was correctly decided: https://supreme.justia.com/cases/federal/us/272/52/#tab-opin...
"The vesting of the executive power in the President was essentially a grant of the power to execute the laws. But the President, alone and unaided, could not execute the laws. He must execute them by the assistance of subordinates. This view has since been repeatedly affirmed by this Court. Wilcox v. Jackson, 13 Peters 498, 38 U. S. 513; United States v. Eliason, 16 Peters 291, 302; Williams v. United States, 1 How. 290, 42 U. S. 297; Cunningham v. Neagle, 135 U. S. 1, 135 U. S. 63; Russell Co. v. United States, 261 U. S. 514, 261 U. S. 523. As he is charged specifically to take care that they be faithfully executed, the reasonable implication, even in the absence of express words, was that, as part of his executive power, he should select those who were to act for him under his direction in the execution of the laws."
The Constitution, of course, imposes limits on executive power, and statutes create private rights and obligations and provide procedures and substantive standards. But if the executive power otherwise may be exercised, Congress cannot constitutionally insulate the exercise of that power from the President's influence. Put differently, the procedural framework of a law can't merely be there to insulate the exercise of executive power from the President's influence.
To address your examples:
> Can he, for example, raise and lower interest rates over the objection of the Fed?
Probably.
> Approve an IPO that the SEC rejected?
It depends. The securities laws regulate private conduct--that's important--and impose various standards and procedures. So the president can't alter private rights without following those procedures and standards. But can the president supervise and direct how the SEC does it's job? Yes. The Arthrex case is relevant here: https://www.supremecourt.gov/opinions/20pdf/19-1434_ancf.pdf.
> Lend money to his supporters through the SBA and deny loan applications from his adversaries? Refuse to deliver Hunter Biden's mail?
No to both, because nobody at SBA or USPS could permissibly do those things.