You will get the best results using a lens designed specifically for imaging two-dimensional flat objects that are parallel to the camera's imaging plane. Such lenses are highly corrected for field curvature to give them good "flat field" performance. Most good prime (single focal length) macro lenses have fairly good flat field performance.

Many other lenses are less corrected for field curvature because correcting for field curvature also impacts other properties of the lens in ways that might be undesirable for other types of photography. For example, in order to render pleasing out of focus areas when using very wide aperture settings, many "portraits lenses", such as the Canon EF 85mm f/1.2L, leave field curvature mostly uncorrected. Even though the 85/1.2 costs about $1,900, the more modestly priced EF 100mm f/2.8 USM Macro (priced at about $600) would be a better performer for photographing flat objects.

I believe depth of field doesn't play here as all the objects are at same distance.

That's a bit of a false assumption. Since the field of focus is never perfectly flat (even in theory with a perfectly manufactured lens), stopping down to increase the depth of field will result in better acuity at the mid-frame and edges/corners of the frame with most lenses.