This is what i would suposed to get from “visible” projection of curve on mesh - visible means that visible from projection plane - besides it should be only one curve since mesh is combined:
let’s say that inverted z axis of gumball is direction in which we are projecting the circle - so basicaly we would project to objects which are visible from circle point of view to bottom.
I added shading to be clear which parts would be seen as visible - basically all surfaces where normal is less or equal to 90deg between direction and normal vector and where curve first time hit srf ( there shouldn’t be project through solid behaviour ).