I'm a military contractor. I have lots of military buddies in almost every branch.
Back in November, my pilot buddies (O3, O4) in the AF received chain of command in contested power transfer briefings. Basically the guy who was in charge last stays in charge until everything is ironed out. Something about the Prometheus protocol (a nickname, not its official name).
My Navy and Army buddies did not receive any briefing like this.
Take this information however you will.
Honestly I don't know. I think by the letter of the law the commanders of the armed forces are obligated to follow orders from POTUS (Trump), but there are many leftists and apolitical types in the military and lower level commanders may not follow orders they believe to be unlawful.