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.
Do you already have an idea of which framework to use and how the result might look like? Is it just going to be a web view, or could it actually have some native elements so that e.g. the back gesture, scrolling hiccups and scroll-to-top could be improved?