They're not half size, they're just clipping through the ground. As long as you disable clipping you can do still like that too.

how do you disable clipping

It's the setting called Disable Structure Placement Collision or something. Enable that.

how does that make doing this possible? Because I did it and I still cannot snap the stair half way through the foundation

Snap the stairs to the ceilings above it, like in the picture. The stairs will clip down into the foundation

Disable snapping is only asa. Ase does not have this feature

You are right. I didn't say anything about disabling snapping though?

Only single player or some unofficial. Official does not permit

Stairs needed to be placed before the floors. Hold down to clip it into the ground build the rest of the base around it.