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
Ug that sucks.
For the data point, I don’t have that issue. Not sure what the difference is. I’m using an iPhone 12 mini and iOS updated to the latest. Voyager works really well for me. Remarkably well.
Clearly it’s a problem many are having based on the upvotes. Hope it can be fixed.