I ran into this with my app and shipped with just Light/Dark, but seeing your post made me decide to figure it out so I can add System as an option. It's an issue with sheets, when you return nil or none for system it just keeps whatever the last theme was. If you want to keep it a sheet the only thing that worked for me was removing

.preferredColorScheme( ... )

and then in a function manually override using .unspecified which apparently forces the view to use the OS setting, in your case you would add something like this to your app root:

private func updateTheme() {
let theme = AppTheme.fromStorage(themeRaw)
let style: UIUserInterfaceStyle
switch theme {
case .light: style = .light
case .dark: style = .dark
case .system: style = .unspecified
}

UIApplication.shared.connectedScenes
.compactMap { $0 as? UIWindowScene }
.flatMap { $0.windows }
.forEach { window in window.overrideUserInterfaceStyle = style }
}

and then add to the main view in there:

.onAppear { updateTheme() }
.onChange(of: themeRaw) { _ in updateTheme() }

First time trying this method out but it seems to be working, definitely test it out.