Get vertexes intersecting points between a 2D polyline and 3D polygon

I have a multiple polygons that represents a ground model surface.

I have one border, that for example marks the limits of a buildable area.

I want an extruded version of my border, using the extruder I for example can extrude it by 10 m up. But I want to extrude it from the height of the overlapping area on the ground model +10 m. That is a separate problem with the vector, however, to do that I need every single intersecting point where the polyline (see orange TOP) edge intersects the polygon, or where the border goes over to another triangle. (see the grey crosses). The border has no z-value or elevation. What I want is a polyline that follows the surface of the ground model and that I can get the z-value for each point or edge so I can extrude the height accordingly.

So the orange is now flat, but I want it to drape over the gorund model and follows its height, so then I can easily add my 10 m.

I tried a combination of Intersector, Surfacedraper, and surfacemodeller but Im having a hard time understanding how the all work togehter so solve my problem. When I draped it just left a cropped version on the gorund surface. I can provide screenshots of the data but I really dont have any workspace atm since I only idea spawned and have nothing there.

I made a nice little drawing in jpeg to help with the question: