https://www.youtube.com/watch?v=IjzhUCl3gXg
Since you're not selecting the enclosed area to extrude (which is how the older RealThunder implementation works), but instead the edges, shapes will need to be drawn out as edges if you want to extrude just their intersecting parts.
e.g. if you wanted to pad only the intersection of a Venn diagram of two circles, you cannot, without breaking the circles into arcs.
You could use the Split Edge tool twice on each circle and then make the two new vertices on each circle coincident. But this can be really tricky to constrain. You could also draw out the arcs independently on top of two construction geometry circles.
As I understand it, this "feature" is largely a consequence of the new TNP mitigation code. You can do other things as a result, like select the edges of a hole on a part and extrude that.
It does not work in the Part workbench yet; that has more possible outcomes for extrudes I guess.
It's now also possible to have multiple separate solids in a single body in Part Design: