This is the kind of thing I could spend hours doing during my college days. I remember the golden days of Android custom ROMs and specifically kept a phone that got a rotating ROM everyday (God bless Titanium Backup).
I think you can use cowabunga lite to theme every app and it won’t have the shortcut notification, but it still wouldn’t have the notification counter on the icon
They either changed how the notification works or made it minimal for models with the Dynamic Island. I just tested a simple shortcut to open an app and besides a little blip on the Island it was no different from opening the app normally.