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
I agree, that’s what the “sort of” stands for. Depending on how the implementation would look like, it might still make some of the small annoyances that I currently have go away (scroll-to-top, back swipe, scrolling hiccup, multiple app icons, haptics, …).