How would/could a sitting President be involuntarily committed?

I’m not asking about suspending the President’s powers; assume section 4 of the 25th amendment has been invoked and the Vice-President is Acting President. So now the President can’t exercise any powers pending a vote in Congress; who decides if he can control his own affairs and treatment? Could he be placed under the DC equivalent of a 72hr hold? Who would decide that? Would it be up to his next of kin (presumably the First Lady) to petition for him to be committed? Does Walter Reed even have a behavioral health unit?

Why would the rules be any different from a regular case of getting someone involuntarily committed?

And it’s irrelevant whether Walter Reed has such a unit - If someone needs care that isn’t available at Hospital X, they’ll just bring him to Hospital Y, no?

Surely such a President can exercise many sorts of powers, like eating, talking, going to the bathroom. His actions just don’t have the legal effect of the President was doing them.