APPEAL TO HIS SISTER COMPLEX omfg... im laughing..... BUT YES i think kaoru would probably also go out of his way to tease beat, but i think that as the years went by it'd probably die down to kind of like... a friendly-ish antagonistic ribbing, the less manic he got. basically kaoru would probably never apologize in a fully satisfying way BUT he would recognize that killing beat is a personal failure of his signifying that he wasn't strong enough to overcome the game. he never had anything against beat to begin with so i think he'd have been able to come to that conclusion within the first year probs!

HE'D HAVE BEEN NO HELP DURING DEPRESSION ERA BEAT but he'd definitely not mind working together with him in dangerous missions because he also has dumb powers. dumb power danger squad. also since he is fiercely defensive of ALL DESTRUCTOCOMRADES EVEN BEAT i'd imagine he'd have extended the offer of learning swordplay to him too.