Wow, there's a lot to unpick in this one! I'm a primary teacher and I'd be massively concerned about a year 5 being so obsessed with stickers. Badges for roles are fair enough (providing everybody get the chance to be nominated to class rep etc) but I've worked in a range of schools (including a prep school) and I can't imagine even suggesting stickers to upper key stage 2 kids. The special jumper thing is weird - I would seriously question what the school is thinking with that.
I agree that it's much better this is sorted before secondary as it could have been much worse.
I also agree that the name Badge Boy won't be being used as a term of affection by other pupils.
In terms of moving forward, your DS obviously needs a lot of support. However, I think you also need to modify some of your behaviours as well. It's fine to listen to your DS when he tells you about school but you now need to have an attitude that is much more supportive of the school, even if this is just outwardly to DS. When he tells you something, don't automatically believe his version is the truth. He is a child and now unfortunately a child who is known to lie. You need to question his role in these situations much more and be clear that you support his teachers and will check with them to clarify situations.
I think you need to decide how you will parent him going forwards. He has been babied to some extent with the sticker situation but then has free reign on his tech. This must be hugely confusing for him. You say you are strict but in what way? Does he have roles and responsibilities at home? Could he have some kind of reward system at home to replace the sticker obsession but also get him used to chores and responsibility?
Check your parental controls on his devices and your wifi. He's clearly had access to unsuitable material and that needs to be stopped. He also needs to be monitored on devices much more closely. Remember that social media and things like YouTube have a minimum age of 13 so check the parental guidance on anything he has been using!
I think PP are right about friendships - does he actually have good friends at school? Or has he created the eccentric character to cover the fact that he doesn't?