You can jump in mid-air when backdashing off a ledge.

You can also get a jump in at the end of the katana's input command, but there's timing involved.

When straight walking off a ledge, yes. It's intended to prevent people who jump at the very last moment from missing their jump.

But there is no reason to have this at the end of any animation that pushes you forward off a ledge like the backdash or katana specials. This is a bug that allows the player to extend their jump distance.