What does happen with smaller formats is that diffraction produces a larger Airy disk measured as a fraction of the film diagonal because the actual size of the Airy disk is a function of the f/ number.

The effect of this increase in diffraction can be taken two ways. You can compute the depth of detail considering that the total blur area of the blur circle is the sum of the area of the circle of confusion and the Airy disk. This leads to less depth of field. Or you can consider that the whole picture’s resolution is degraded by diffraction and use a correspondingly larger circle of confusion to compute the depth of field resulting in a larger depth of field although you have less total detail in the image.