That's Commander in Chief, on Jan 21st 2021 that could change, Nov 3rd 2020 can't get here fast enough. No the military does not swear an oath to a POTUS.You don't fully get that whole "Command and Chief" thing do you?
Yes, I swore an oath to defend the constitution way back in 1981, and re-affirmed that oath several times over my military career. But in every Army building that I ever walked into that had offices for people in positions of Command, there were pictures of every Commanding Officer in that chain of command and every single collect ended with the President of the United States of America.
Do you think that was just for show?
Sorry but you don't swear an Oath to a higher Commanding Officer, the US does not do that, one shows respect with a salute and it's returned as is proper, I was in NJROTC before the Army, there was no AJROTC where I lived at, I was an Officer.