Remember Firefox web shortcuts do not show an icon ?
And also see Utility to create and manage « web-apps »? nobody ever answered there…
Chromium has already something like this, natively → which creates real launchers on desktop ( and not only links ) → under other tools, create shortcut.
Firefox should soon propose some equivalent tool, as it already exists in FF for Android.
ICE works fine - needs some additional care in case of snap ( chromium ). Any thing snap always needs additional care anyway.