This is referred to as “standalone” mode, and it explains why, every time you tap on a shortcut icon from the home screen, you see a splash screen for a second before the associated action is launched ...

Go to your iPhone's home screen. Touch and hold the background of your home screen until the app icons jiggle. A screenshot ...

The Finder trick and Replacicon have been around for a while, but in macOS Sonoma, similarly to what was already possible with Shortcuts, we now have the option to pick any image file as a custom icon ...