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
In my opinion, it’s been great and feels pretty close to native anyway. Some issues with the screen freezing when trying to scroll after swiping away from a post but other than that, it’s super nice. Plus updates are so quick to install, really like that too.