It’s fairly secondary to the story-telling but, I agree, it’s relatively important background information when your story revolves around a structured organisation with hierarchy and ranks or grades for the characters.
Much easier to establish the background structure and give the writers / directors / actors a clear frame of reference.
In fairness, it looks like they’ve actually done a pretty good job of working this up, even if the flag officer rank titles on that one page were a bit goofy. I suspect that will all get corrected in due course.
Trek has always had script and wardrobe niggles with rank titles and rank insignia, so much so that it’s practically a tradition (!).
Twenty years ago, things like this would have bugged the s**t out of me; these days, real life concerns are waaaaaay more important to me and I just enjoy the episodes for what they are. I still like discussing the minutiae of the uniforms and insignia — but I’m not going to lose any sleep over it...!