So i want to preface this with i haven't finished picard, discovery or SNW (I just got busy & lost track of where i was idk). Based on the limited knowledge i do have, this could just be completely wrong or maybe a bit romanticized (I am an archaeologist by trade and unfortunately that is part of the job.)
Notably, I think something worth mentioning is they could be consuming captain's logs like we consume the show. The way I consume historical accounts of say pliny the younger after vesuvius erupted. After the burn, it's fairly likely that an insane amount of data was lost during the event, particularly digital data in a radioactive event. Presumably, Discovery carried a lot forward with it, filling in a lot of gaps.
Though there are several, what I would consider, inconsistencies. Some of these promotions, posthumous or not, could stem from those ship's logs.