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
Well… Part of that is just that web apps have much worse efficiency and performance compared to native apps. That’s not to say their performance and efficiency is bad, but a native app will beat a web app everytime. The DOM and JavaScript are just not great models in terms of efficiency and performance.
Problematic
I get lots of random freezes, actions not registering, etc
Doesn’t make it unuseable, but it’s not a great experience
I think it’s acceptable, though I am working on my own … for now experimental … Lemmy client in C++/Qt/QML … maybe eventually for desktop and mobile devices alike :)