# "Merge by Distance" is destroying information about double-sided polygons

I have a mesh in which I want all of the faces to display as double-sided (after exporting to a game engine), so I duplicated the mesh with Ctrl+D and flipped the normals. Then I figured I'd optimize the mesh by getting rid of duplicate vertices, so I went into Mesh -> Clean Up -> Merge by Distance. The problem is, this destroys the double-sided faces that I just created.

I'd rather not duplicate the vertex information, but still have triangles be double sided. In computer graphics terminology, triangles with different winding orders, for example, vertices A, B, C would have triangles [A, B, C] and [C, B, A]. Is this possible to do in Blender?