We have 2 threads about this.... a new test to show if a person has SFN... by observing the winkling of the finger pads in response to Lidocaine applied to them.

However our search function about this topic brings up our old addy location for them which is broken since we moved to a new server over a year ago.

So here are some links explaining that nerve damage to the hand does not allow wrinkling to occur.
Case of the month: The skin wrinkle test: a simple nerve injury test for paediatric and uncooperative patients

Evaluation of the finger wrinkling test: a pilot study
As you can see, the results can be spotty.

This article discusses a new test using Lidocaine applied to the fingertips. There is a good photo of the grades of reaction of wrinkling in this link about the study done.
Evaluation of the finger wrinkling test: a pilot study
I found this link however difficult to really understand. No wrinkling is indicative of nerve damage, it seems.

When I did this test here, my left hand had wrinkles and my right did not. This corresponds to my long history of carpal tunnel. But lately I have had a flare to my left hand of nerve pain which I thought was a sprain of some sort. The wrinkling which I had commonly is now gone.

Your increase of wrinkling may be addressed here:
Wrinkled Fingertips Causes, Without Water, Thyroid, Diabetes, Dehydration, Lupus, in Water, Treatment

The photos in the above link appear dramatic to me. I've never had wrinkles like those shown to that extent.

Do you have this degree as in your photo, equally in
both hands?