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
With a capacitor app it can be both a PWA and a native app from the same code base. This wouldn’t take away, only add possible functionality for those who choose to install it natively.
There’s a lot of native functionality that a PWA cannot access, like app icon changing, certain gestures that Apollo took advantage of (tapping on the top to scroll to the top, for one), and some other things that have been requested.
I would be so happy if we got Apollo-style scroll to top. That’s the one thing I’ve really been missing
Fair enough, thanks for explaining.