I don’t think this will matter much, because of the second line there:
Deputy Secretary of Defense Kathleen Hicks has picked up his duties in the meantime
One of the big themes of Trump vs. Biden (or anyone else, really), is that Trump is utterly incapable of creating a government that works. How many cabinet positions changed in his first term?
The whole point of Biden, and normal functioning of government overall, is that you’re not reliant on The One Guy. You have people in place to take over the job if something goes wrong, and you can trust that those people are probably competent enough to do the job, because they were appointed by people who took continuity of government seriously.
The only thing Trump would care about is if the person was personally loyal to him.
So, let them keep things like medical issues private (as they should be), because they have a team in place to get the job done, regardless.