I really hope the show doesn't wander off into the weeds exploring the details of its fictional setting, which is scribbling in the margins. It was when Trek started to take the Federation seriously that it started to deteriorate, at least partly because the folks involved seemed to be either satisfied with - or else found it expedient in order to avoid audience confusion - to based everything about the alleged future off of the closest contemporary or recent historical analogy they could. So we wind up with a Federation Charter "Seventh Guarantee" which maps directly to the Fifth Amendment to the U.S. Constitution.
Keep everything vague, general and in the background. I do not care how many planets are in the Union or any of that nonsense.*
*I was told while on a story assignment that Gene Roddenberry deliberately refused to define the size of the Federation - "It could be ten thousand worlds, or two dozen" - which was fucking brilliant. Sadly, not long after his wishes ceased to be a factor we were given a number, which was of course based directly on the number of U.N. members.