Selecting the sex of the PC has been a standard feature in practically every RPG with character creator ever, and definitely in Bethesda RPGs, what they added is an option to change pronouns the PC is referred to by NPCs from the default. If you want them to match you simply don't touch that option, done.

From a developer's perspective it's dead simple, similar in triviality as allowing people to mix+match any voice to any body type. Cyberpunk's free choice of genitals needs some implementation care but if you're planning for it from the start it's also easy.

Where things get more complicated is things like dresses for male bodies, especially if you don't have any shape keys in place. But if you use one body mesh for everything and simply shape key it into male and female then it's again no issue (you also need to lerp animations then, probably, male and female bodies walk differently because hips). Basically it's hard if your asset pipeline is simple, if the pipeline is sophisticated it's easy.

If so, my only remaining question is if one were to use the mod, does it mean others not using the mod can’t see their pronoun(s)?

It's a singleplayer game. Nothing you do can have any effect on the experience other people have with the game.

I think this is the reply that prompted me to reply at the top of the post. Does your edit mean I was of some help? You appear to have the right of it, yes.

As to your second question: what mod loadout a player has will have zero bearing on another's experience. If one were to use the mod, others would not be affected.