Is it possible to get the app icon of a built-in app on iOS?
In a word, no.
Not on iOS as there is no way to get to that particular icon without jailbreaking the device.
However there are 3rd-party tools (iMazing is one of them) that allow you to copy apps from the phone to the Mac and explore the filesystem on the phone.
Not sure if they will give you what you want but I do believe that the apps that do this have demo modes that will let you find out.