The president is requried to do things, but…
If the president refused, what would happen? Nothing, you can pass law after law saying he has to do things, but if he doesn’t there’s very little you can do. In fact the only thing you can do is impeach him and remove him from office.
If you look back to when some states tried to pass a law for term limits, the US Supreme Court said, “No.” You can’t add on additonal requirements. When states tried to prevent convicted felons from being Senators and Representatives, again the SCOTUS said, “No.”
So while in some states convicted felons can’t vote for themselves, they can, in all states run and be elected as Senator. Of course the US Senate or House can simply refuse to seat that elected person.
As for the example:
reimbursing the government for the cost of food served at the White House residence.
This may be so, but what if the president refuses. What’s gonna happen? Nothing. Does he stop being president? No of course not. I suppose you could try to bring civil or even criminal charges against him, but it won’t stop him from being president.
Even Andrew Jackson’s famous “The Supreme Court made that rule, not let THEM enforce it” shows there’s little one can do.
Theodore Roosevelt want to send the US fleet on a show of strength when he built up the navy. Congress refused to give him money for this, calling it wasteful. Roosevelt just ordered them to go anyway. Halfway around the world the fleet ran out of money. Then what could the US Cnngress do? They could leave the fleet where it was stranded or allow the money to be appropriated, which they did.
In Congress it’s a bit different, just a bit. The US Constitution give both houses the power to set rules for its members. So either house could pass a “rule” requiring drug testing and then refuse to seat a member who didn’t pass the test. Of course they can’t stop anyone from being elected, but they can refuse to seat that person
The only thing I can think of off hand the President HAS to do, according to the US Constitution is give a state of the union address. Though I’m sure there are a few other things in there I can’t think of at the top of the moment.