Here's an analysis of my image in the different "wings":

Analysis of my image

The foreground (wing 1) is determined mostly by the DOF

The second (2) wing is determined mostly by the presence of textural detail and microcontrast.
Note that the quality of the lens plays a key role here. The lens must be able to render good microcontrast to bring out detail from a uniform field of grass. Also, and more importantly, the lens has to have a smooth bokeh-to-focus transition, which is the case here, because a good gradual transition makes you "feel" the depth better

The line of trees (3) is the third wing and it coincides with the focal plane.
It therefore has to contain the most textural detail and this is the part that benefits more from a little sharpening if appliec wisely. An unwise sharpening would add too much detail to (2), thus making the planes flatter. I think I have been good here, I only sharpened just as much as it was needed to balance the AA filtering of the camera. It was a conservative sharpening, that left he way the lens has interpreted the reality, substantially untouched.

Behind the line of trees we have wing four (4) which is the most amazing part of this image in my opinion. Why? Because I shoot this one with a 135mm, which, normally, would just flatten out everthing that is beyond the focal plane.
Here, instead, we can perceive a clear spatial difference not only between (3) and (4), which is normal, but also between (4) and (5), which is NOT normal, and this shows well I think the importance of having those expensive lenses. A normal 135mm would not have brought this out I think. The Elmarit did.

Behind (4) we have two wings of hills, (5) and (6). Here, the Leonardo aerial perspective enters powerfully the play.
Note that the more haze, the less textural detail and the less macrocontrast also.
There is a big different in the macrocontrast of (3) and that of (5) and (6), like we were actually looking at two images made in separate moments, but they are all there at the same time. So yes this is a lucky coincidence where the haze helps, but I think I have shown that from (1) to (4), we have also great great depth perception without the haze playing any role.

So my conclusion after this analysis is that depending on the part of the image, different elements may enter the play and add (or detract!) from the perception of roundness.

In other words, it's not only a concept of "this does that and this does not", but also a concept of "where".