One property of spatial infinity is that all spacelike geodesics end at it. Since spacelike geodesics can have different directions, I do not understand why spatial infinity is a point. It looks more like a 2 sphere instead of a point.

I will provide more information. Let us pick a point other than the spatial infinity in the conformal diagram. Usually, people draw the conformal diagram in a plane or represent it on the surface of a cylinder. So this point on a plane represents a 2 sphere. But spatial infinity is literally a point. Why?