Sorry I can’t understand your message completely. Are you asking for examples in which the app icon does not revert back to the original after quitting?
I’ve tried Mac Catalyst apps like Mona which offer app icon customisations but same as Bear, they revert back to the original app icon when quit.
Craft takes a unique approach to this. It displays the app icon options in the UI, but when clicked on one, it redirects to documentation on how to change Mac app icons manually at the system level which prevents it from being changed when the app is quit.