I have one Pwa installed and it seems to be working automatically - at least at some points. Setting appearance to automatic (and iOS dark mode on) shows a automatically generated dark mode version of the icon in notifications and in settings. The home screen icon stays light though. Tinted appearance is working on the home screen, but then the notification icon stays in light mode, regardless of the iOS dark / light mode setting. Settings icon is working fine though, so automatically switches between dark and light. Tested on iOS 18.0 stable, iPhone 13.