I noticed the same thing, but likewise forgot it. Years ago this turned out to be a problem for me because I designed and made my katana stand to look better if the katana is in it the wrong way. But it couldn't be helped, I ended up putting the sword there correctly. Since you need a license to own a sword in Japan (and those licenses have special, enforced requirements), maybe Japan has reached a point where even many Japanese don't know anything about this.
If you purchase or inherit a katana that has cultural or historical significance, which is the only way to get a license for it, one would assume the owner would also know a bit about such basic cultural customs and beliefs. Of course we don't actually know if the mangaka did it here on purpose or accidentally. Maybe Yuuki personally doesn't know anything and the mangaka wanted to illustrate that by having him place the sword the wrong way in the stand.