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
Such as?
Don’t get me wrong, it’s still impressive. But I‘m very aware that it’s a web app and I have to step carefully. These might be small things, but they’re constantly annoying me.