Projecting a drawing onto a complex curved surface

I’ve seen similar topics but none of the directions work for me. I have an object with many different curves making up it’s top surface.

I have a drawing above it that I want to project onto the surface and then extrude only the part of the drawing inside the perimeter down into the object just a small amount. Crucially, the bottom of the extrusion needs to follow the surface contour of the part, not have a flat bottom.

My understanding is that I need to select the drawing, click project, and then select the object. But when I try that I just keep getting “Something went wrong but your project is intact”.

I can’t get to the step of figuring out how to extrude the drawing down into the part following the surface contour, because I can’t get even the drawing to project onto it.

Please, please if someone could walk me though this like you would with a 5 year old I would be eternally grateful.

Can you share the project?