It looks like ResourceFunction["Torus"] is defined by creating a tube around a BSplineCurve. The default CapForm for Tube is "Round". So, I believe that what you are seeing is the overlap of the end caps of the tube. FWIW, in version 13 Torus is a built-in function, so no need for the ResourceFunction.
CapForm[None] did the trick with no downside that I can see.
Graphics3D[{CapForm[None], Opacity[.2], ResourceFunction["Torus"][origin, {10, 1}]}]
