The control of material mapping in AutoCAD is very awkward and I can understand your frustration. The challenge is increased when working with an image like a circle where you do not know what is up or down or if the image is rotated. Sometime I apply the standard checker material to get a feel for how the mapping is being applied. For example, in the image below you can clearly see that where the seam lies.

Since the radius of your cylinder is 100, the circumference is about 628. Entering this for the width yields.

Switching back to referencing your circle image yields.

and the circle is clipped at the seam. Now you would think, or at least I would, that you could could edit the offsets and scale and get one image. I tried with little success. Note that if Tiling is set to none, two tiles appear when there should only be one.

This leads me to the conclusion that there is a bug in AutoCAD (2023) with cylindrical tiling.
You could experiment with an image that has a larger background but my advice would be to use 3ds Max which has exceptional controls for material mapping. AutoCAD material mapping is just too primitive with an awful user interface.
lee.minardi