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
Personally, I would like to see a Native App. I get that this PWA makes it easier to develop for both Android and iOS, but there’s something about Native apps that just seem like a better experience to me.
I think it’s mostly the interactions that feel a lot snappier in native apps