I haven’t examined all the ethical and practical issues, but my initial thought is that we need to change the law.
All leadership in Congress, the Chief Justice, the cabinet and other head-of-department personnel ought to be reported as unavailable if they are going to be out of commission for a few hours or more.
If there is a privacy matter, or judgment calls, there should be a designated official in the White House and Congress who is told.
Maybe it’s always
1/ the personal physician to the President,
2/ the chief of staff,
3/ the President if he is available/awake, 3/ the physician to Congress,
4/ the speaker of the house,
5/ the VP, and
6/ the speakers pro temp of the senate, and
7/ the Chief Justice or physician to the court.