I just tried it with "Bilinear" and "Bicubic", and the result looks much better.
So, there seem to be two issues:
1. "Lanczos 3 (non-separable)" creates the double outline artefact.
2. Resampling does something, even though the original image was 640x640 and it was also exported to 640x640. Does that not make resampling obsolete?
P.S.: I guess I'll just use Bicubic then, since that sampling method is superior to bilinear. However, maybe it's still worth looking into, I guess. Either there's a bug to fix in the sampling code, or the help could be amended with a notice that Lanczos is maybe more suitable for photos, and less for line drawings?