I created an AppleScript which executes a simple Python file.
I've given it full disk access but still every time it runs it prompts a "X would like to access files in your Desktop folder" message.
AppleScript has historically saved all properties and globals by writing to the script file, so the security system puts up the dialog again because it is seen as a different app - one that hasn’t been given permission yet.
The solution is to code-sign the app (you can use a self-issued certificate), or otherwise make the script(s) in the bundle read-only.
do shell script
which executes a python script. I exported it as an application file format and Run-only as the option.