This is just a reasonable guess that I have never seen tested or specially tested with lenses that have been heavily corrected for field curvature and astigmatism that are closely related.
Most lenses that are highly corrected for field curvature are used for macro works or for reproducing flat two-dimensional documents / graphics. "In such cases, the aesthetic properties of the background blur do not play a major role in lens design.
Lenses with uncorrected or undercorrected field curvature often also show sagittal astigmatism. The two things can be combined, especially when used with a moderately wide lens with a very large aperture, resulting in mechanical vignetting. This can lead to a "whirling" type of bokeh, often referred to as the "Petzval effect".
Most lenses that produce such "vortex bokeh" involve some form of mechanical vignetting.
The widely opened opening on the left shows mechanical vignetting when the entire entrance pupil is not visible because the tube of the objective blocks part of it from an area still within the field of view of the objective. Even without significant field curvature or astigmatism, such a lens exhibits "cat's eye" bokeh.
Add an uncorrected field curvature and a scene with lots of bright, blurry lights to the equation. For example, a bright sky behind foliage, and you get the "vortex bokeh" effect.
What is this vortex-bokeh technique and how can I achieve that?
What is the cause of this uneven bokeh effect?
On the other hand, if the lens is greatly corrected for field curvature to give it a more or less flat focus field¹ and the lens also has tangential astigmatism, the shape of the bokeh will appear to be radially stretched from the center of the lens as in the example photograph shown in the question. By greatly correcting field curvature, the astigmatism may shift from sagittal (if FC is not corrected) to tangential. When the sagittal MTF is higher than the tangential MTF, the tangential lines are blurred than the sagittal lines and therefore propagate in the direction perpendicular to these tangential lines over a larger area.
What most of us view as "good" bokeh in terms of the quality of the fuzzy highlights is the lens design, which does not or only insufficiently correct field curvature and / or spherical aberration. This means that such a lens is not the best candidate for other types of photography, such as: Landscape or architecture, if we want a good sharpness to the edge of the frame.
The classic example of this is the Canon EF 85 mm 1: 1.2 L II. What makes it so great is the uncorrected field curvature it shows. This makes it a totally unsuitable lens for flat reproductions or taking flat test charts, as the focus field at the edges and in the corner in front of the flat subject has a considerable distance when the center of the lens is perfectly focused on it. If you want to capture a perfect photo from a flat test chart, the floor will be absolutely clean with the $ 350 EF 85mm 1: 1.8 with the $ 2,000 EF 85mm 1: 1,2 L II. But if you want to have this fascinating bokeh on the edges of a portrait, there is nothing better than the 85 / 1.2!
¹ Note that most lenses have some field curvature. The focus field is not a perfectly flat plane, even with a theoretically perfectly manufactured lens. Lenses that are strongly corrected for field curvature, such as Many macro lenses, for example, still have a focus box that looks more like a Lasagne as a flat plane. They are not perfectly flat, they are only flatter than uncorrected or less corrected lenses. To learn more about the subtleties of the focus field, I recommend reading Roger Cicala's excellent series:
Fun with focus field part 1
Fun with Field of Focus II: copy-to-copy variation and lens test