Set the overhang parameter in Blender 3D printing tool box
You are looking at overhangs in the design tool.  What matters are overhangs when printing.

When designing the object, the coordinate system is convenient for working with the object.  Before slicing, the object can be rotated and repositioned for better printing.  Only after is it positioned for printing can the actual overhangs and bridges determined.

Unless you wish to limit yourself to the design tools coordinate system, I wouldn't have the design tool generate support material, and I would ignore its comments about overhang angles.  First, bring the object into your slicer, position it on the print bed, and only then evaluate the need for support material.

To be honest, I often have a printing strategy in mind while I am designing an object, but when the object hits the printer I sometimes completely change my plan.