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
Many people have not heard of web apps, they do not know how to find or install web apps.
Most of them are more familiar with the app stores. They are more comfortable using what they are familiar with. They might have been using the app store since the original Angry Bird was released.
It is good to have choices.
Yes, I think even if it’s just a wrapper and nothing else changes other than the app being in the App Store, that’s probably worth it because you’d get more users.