Wacom Center uses the Screen Recording permissions to take a screenshot of your desktop when the Mapping or Display toggle pages are opened. It then places thumbnails of each display’s content on the respective tiles and graphics on those pages. This makes it easier to identify the displays and how the Mapping or Display toggle functions will be applied. The Screen Recording permissions are not used for any other purposes.
If you deny the Screen Recording permissions, it will not affect the driver or Wacom Center functionality. However, the display thumbnails on the Mapping or Display toggle pages will only show a generic graphic and you will have to rely on the name of the display to understand the settings (e.g. the selected Screen area, or the Display toggle sequence, etc).
To grant Screen Recording permissions to Wacom Center, open macOS Settings, go to Privacy & Security, Screen Recording, and enable it for Wacom Center: