Honestly, you don't have anything to apologise for. I'm doubting those appeals you handled got overruled by an HA or higher?
So don't apologise for anything. You did what you thought was wrong. if those admins then decide he should have been stayed banned they can take it up to HA+ for an overruling. If anything those people should be apologising towards you as they clearly don't know how the appealing system works.
You've been wrongfully punished with an official and now you're apologising towards everything you did. Don't mate. You merely deserve a slap on the wrist.
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