Saru is the highest ranking officer aboard the Discovery. Starfleet protocol makes him Captain. He also has the consent of the rest of the crew which technically isn't necessary but the whole lost-in-time-and-space makes it more practical. Janeway had to negotiate with the Maquis to keep her Captaincy aboard Voyager when it was displaced into unknown territory. She didn't have to do it but it made things easier to replace the deceased FO Cavit with Chakotay instead of another Starfleet officer.
Science Officer Michael Burnham is the lead character of Discovery just as Captain James Kirk was the lead character of the Original Series. Why is this so difficult to grasp?
Again its now refreshing to see Discovery as a proper Star Trek series instead of a decent sci-fi action/adventure written by Star Wars fans. Disappointing that it took them till season 3 to figure this out but I'll take it anyways.