If you care about diffraction blur relative to the size of the object being imaged, then physical aperture is all that matters. [This] quantity might loosely be called angular resolution. If I take a picture of a distant tree, and I want diffraction to be small, compared to the size of a leaf on that tree in the final print, then I care about angular resolution.

Agreed to this point: the "physical aperture"* (a.k.a. entrance pupil size, a.k.a. effective aperture diameter) effects the "angular smearing" of the light.

The next question is how DOF comes out, particularly in this special case of macro photography. I know that at normal distances, the circle of confusion size relative to image size also depends on the effective aperture diameter when subject distance is equal, but in addition it varies inversely with the [square of the] subject distance, though these rules vary at very close range. If I have remembered that right, then using a longer focal length at equal effective aperture size and also using a greater subject distance to cover the same field of view will give equal "angular" diffraction effects but also more DOF, which sounds like an advantage for macro photography. (This is to be balanced against the need for a longer exposure time and/or a higher exposure index.)

* Aside. AFAIK (please correct me if I am mis-rembering any part of this!) it is not quite the actual physical diameter of the aperture opening that counts, since its position along the optical path also matters: the same sized physical opening closer to the focal plane produce the same angular smearing leaving the aperture but therefore less smearing at the focal plane. This also corresponds to a larger effective aperture diameter and so a lower aperture ratio.

aperture ratio = (distance from aperture to focal plane)/(diameter of the aperture opening)

effective aperture diameter = entrance pupil diameter = (focal length)/(aperture ratio)

with some possible corrections in the macro regime due to the focal length shift in that situation.

The various measure of aperture size agree for the simplistic case of an objective [so-called "lens"] with a single lens [so-called "lens element"] with the aperture size being the diameter of the allowable light path through that lens itself.