Not saying this isn't a trashy edgy-wannabe isekai (that I'm gonna read anyways because I have no self control and like assassins, which don't appear that much in isekai genre),
but that isn't really a katana, even if they called it that.
Kogarasu Maru or Kagarasu zukiri is the name of a type of blade made before katana existed, so it technically isn't one.
For a katana it's pretty small, being around 60 cm, and the only reason for using a smaller blade, is for when you are in closed spaces. In a straight duel, range plays a big factor (as long as the balance is good), of course you can't go against someone with a longsword when you have a dagger, unless the other person is stupid and let's you come close enough that he can't use it.
Anyways, the point is that nothing fucking matters, it's fantasy and there's magic, super speed, huge gaps of power and all that shit. Rule of cool trumps anything, and a medium sized, doubled edged black tachi seems pretty cool to me.