It is a limitation of a PWA. A native app (wrapper) will likely be coming though, and a custom Capacitor plugin could theoretically interface with the native API to switch out icons. Theoretically. No promises though :)
Quoting this comment by the dev
What makes it better than PWA?
Some functions are not open to PwA such as tap top of the screen to go back to the top, icon swapping, updates without deleting and re-installing (which deletes all you preferences) and some other iOS API functions.
You don’t need to delete and reinstall.
Well if you wan to change the icon you do.