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Are you being facetious? Presumably the APO treatment will rid the lens of a bunch of unwanted colour in the plane of focus.
I am being a bit facetious, but mostly serious. It is not at all clear to me what people here mean by APO.
Apochromatism is a design strategy that can be used to improve the MTF. If we assume that Zeiss adopts the strict definition of APO, we are talking higher resolution, higher contrast, more sharpness. Less colour fringing in the plane of best focus is implied, less colour fringing in the blurred parts of the image is not implied but can be expected.
Your unwanted colour in the plane of focus is just one aspect of APO. I translate a sentence like "To me, the main reason to get the ZE 135 is APO, not bokeh or sharpness" as "To me, the main reason to get the ZE 135 is APO, not APO or APO".