Am I Dumb?

[Kaedan]

The first one (you are unfamiliar with katanas).

Katanas are always positioned with the curve up, so that the blade edge does not rest on the interior of the scabbard. That would needlessly dull and damage the edge.

As for drawing the katana, there are multiple "correct" ways to do it. The scabbard is grasped and then twisted in the appropriate direction for the appropriate draw.

In the case of FF14 Samurai, they are using Iaijutsu master-type samurai. Meaning they strike in the same motion as they draw the blade. "One Draw, One Cut." For a rather romanticized example, you can watch Ruroni Kenshin, which is the image in which Yoshi-P based samurai off.