The President is literally the Chief Executive officer in the United States.
https://people.howstuffworks.com/president4.htm
> Laws and budgets are set by Congress
That's correct, under Article 1, but the President does not have to spend every dime that was allocated.
> EOs do not have the force of law
"Both executive orders and proclamations have the force of law, much like regulations issued by federal agencies"
https://www.americanbar.org/groups/public_education/publicat...
You seem to underestimate the power that is vested in the office of the President as the Chief Executive.
> have been invalidated by courts
As have many, many legislatively-passed laws; this is simply checks-and-balances and allows the judiciary to act on other laws (which originate from Congress) and regulations (which originate from the Executive Branch).