I have no idea why you would think that making a new account after being banned means that you've done nothing wrong? A new account doesn't actually mean a new start lmao. Pretty sure this is a spicy troll, carry on.
Certainly, if your only violation of rules is a new account (idk if this is a violation), then you shouldn't be accused of using an offensive word or having been not nice. But so far we, other players have no material to settle who's right. Ask the other moderators.
I don't want to comment on your case in particular because you're obviously already pretty committed to not breaking the rules.
Warnings do not have binding power (it's not a strict strike counter system) but usually only used as a reference if a (light) offense is not strong enough to warrant outright punishment and placed in the hopes that the user will be aware of the rules. Mistakes happen from time to time, especially when you put in robots that are trying to help us into the mix.
Try to forget it; If you behave (and I am not trying to assert the opposite here), you won't be punished. It's that simple.