This is just an enlightened guess that I have never tested or seen specifically tested with lenses that have been heavily corrected to account for the curvature of the field and the astigmatism, which are intimately related.
Most of the highly corrected field-curvature objectives are used for macro work or for two-dimensional flat document / artwork reproduction (or for very good results on flat test diagrams at close distances so that the seller can declare that they possess the clearest possible goal his class. ") In such cases, the aesthetic properties of the background blur are not a primary consideration when the design of the lens.
Lenses with uncorrected or under-corrected field curvature often also show sagittal astigmatism. The two elements combined, especially when they are used on a medium wide lens with a very large aperture resulting in mechanical vignetting, can produce a type of "swirly" bokeh often called "Petzval effect".
Most lenses that give such a "swirly bokeh" involve a form of mechanical vignetting.
The large opening to the left presents a mechanical vignetting, when all the entrance pupil is not visible due to the fact that the body of the lens blocks a part of it from an area to always finding in the field of vision of the lens. Even without any appreciable amount of field curvature or astigmatism, such a lens will demonstrate a "cat-eye" bokeh.
Add to the equation an uncorrected field curvature, as well as a scene with many blurry reflections, such as the shining sky behind the foliage, and the "swokely bokeh" effect.
What is this swirly bokeh technique and how can I achieve it?
What is the cause of this non-uniform bokeh effect?
If, on the contrary, the lens is strongly corrected for the curvature of the field in order to give it a more or less flat focus field¹ and that it also has tangential astigmatism, it seems to me that the shape of the bokeh would be stretched in a radial direction from the center of the lens, as shown in the example picture included in the question. By strongly correcting the curvature of the field, the astigmatism can go from sagittal (as when FC is not corrected) to tangential. If the sagittal MTF value is greater than the tangential FTM value, the tangential lines will be more blurred than the sagittal lines and will therefore be spread over a larger area in the direction perpendicular to these tangential lines.
What most of us regard as a "good" bokeh, in terms of the quality of the fuzzy reflections, results from a lens design that leaves the curvature of the field and / or spherical aberration under-corrected or not. This means that such an objective will not be suitable for other types of photography, such as landscapes or architecture, when we wish a good sharpness up to the edge of the frame.
The classic example is the Canon EF 85 mm f / 1.2 L II. What gives him such a big bokeh, is the uncorrected field curvature that he shows. This makes it a totally inappropriate target for flat reproduction jobs or for flat test cards, as the focus field at the edges and in the corner will be considerable in front of the flat subject when the center of the goal is perfectly developed. above. If you want to take a perfect shot from a flat test pattern, the $ 350 EF 350/350 EF filter will absolutely clean the floor with the EF 85mm f / 1.2L filter at $ 2,000. But when you want this bewitching bokeh on the edges of a portrait, nothing like the 85 / 1.2!
¹ Keep in mind that most lenses have some field curvature. The focus field is not a perfectly flat plane, even with a lens theoretically perfectly manufactured. Highly corrected targets depending on the curvature of the field, such as many macro lenses, retain a focus that is more like a lens lasagna noodles than a flat plane. They are not perfectly flat, they are simply flatter than uncorrected or less corrected lenses. To learn more about the intricacies of the field of concentration, I recommend you read Roger Cicala's excellent series on this subject:
Have fun with the concentration field, part 1
Fun with Field of Focus II: Variation from copy to copy and objective test