Thanks to Reddit I just figured out that the stick inputs are pretty generous. Each of the eight directions will be triggered by the two surrounding directions, meaning each cardinal direction also includes the surrounding diagonals, and each diagonal includes the surrounding cardinal directions.
In other words, if you see an up input, it is triggered by up+left, up, or up+right. Dual inputs seem a bit more strict, though, as while they’re just as generous with what directions count as correct, the two sticks should still be going in the same direction. I was able to trigger a dual up input by pushing both sticks up+left, but pushing one up+left and one up+right resulted in a “Bad.”
I don’t know if different controllers work differently, though, so YMMV.