Well, it is "Special Operations" not "Section 31 badge.Agreed. Section 31 is a shadow organization, not one that everyone should know about... to the point they have their own special badges that people identify. It's one of the main reasons why I rate DISCO season 2 so badly.
People did not know what the badges meant. Hence the confusion.
31 has to have legitimate ways to operate in the open and existing chain of command otherwise it makes things needlessly complicated. Having legit ways to operate makes sense and is tropey as well (just watch MASH, NCIS, JAG, etc.) to see intelligence operatives claiming to operate in the shadows, yet using legitimate agencies as fronts.
Controversial opinion: I'd rather Section 31 over Klingons.It's when we see them every week for a whole season of a series or they take the main villain role in a movie that they just get tedious.