It’s my understanding of naval tradition that the person in charge of a vessel is the captain, even if they do not hold the officer’s rank of captain.

Correct - there is some confusion here with people confusing a rank of Captain with the position of Captain. Both these roles are typically vested into a single individual however command and captaincy can be delegated to another individual, regardless of rank.

In theory you could have a much lesser rank granted captaincy of a ship for the duration of a specific mission. Not common but might happen if a situation requires a specific individual to fulfill that role. In turn, that individual could have higher ranking crew assigned to work with them and they would have to submit to the assigned captain's authority even if they were just an ensign. But this authority would only extend to matters of the ship and the mission at hand, all the person is doing is able to do is act within the terms of whatever authority the actual captain (or Starfleet command) has granted them.