The "Test" use used is not a valid test for turned edge. It does not really tell you anything about a turned edge. A turned edge will not show in this way. It does nothing to make the the star look rough. Nothing at all.
The test for turned edge is done at between maybe 10 to12 waves of defocus.
When you defocus to this level, what you are looking for is the difference in fineness between the interior rings. If there is a turned edge, you will see that the rings are kind of fat and soft on one side of focus and thin and fine on the other side of focus.
This is why I used to urge people to read a book on star testing. It is very powerful but if you listen to people that don't know how to do all of the tests properly, you get bad advice.
You have given yourself a lot of anxiety by not understanding what you were doing. Sorry to sound so curt about it, but I have seen far to many people go down rabbit holes for no good reason other than bad advice.
If you do the proper test for a turned edge and you see that you actually do have a turned edge, the next step would be to use a Ronchi grating. While the Ronchi grating is not really useful for Spherical Aberration without using it in a double pass, if you can see a turned edge using the Ronchi in a single grating test, then that says you absolutely have a turned edge, and you can use the result of the test to estimate where you want to mask. You want to preserve as much aperture as possible, so this means that you want to mask no greater than the break, but sometimes it is best to stop somewhere between the break and the edge depending on the width of the TE.
But I am talking as if you actually have a turned edge and until you do the proper test for a turned edge, you really don't know if you have a turned edge or not.
Surface roughness is more likely but even here, without seeing an image of the problem, it is impossible to say.