Then we STILL haven't seen Federation/Klingon First Contact because in Discovery they've already had some contact. Earth's first contact with Klingons doesn't count any more than Vulcan, Tellarite, or Andorian first contact with them and we haven't seen those either.The context of his statement coincides with his first contact mission in the episode, sanctioned by the Federation. The ‘we’ in his statement clearly refers to the Federation, because that’s what he’s representing.
Maybe T'Kuvma was at Fed/Klingon First Contact and got ticked off, leading to the events of Discovery. Although T'Kuvma didn't seem that old in Disco so official contact happening almost 100 years after Enterprise, while not impossible, is strange.