Add this enum

enum ColorSchemeSetting: String, CaseIterable {
    case light, dark, system
}

Then you can use

struct ContentView: View {
    //@Environment(\.colorScheme) var colorScheme Do not need this!
    @State private var chosenColorScheme = ColorSchemeSetting.system

    var selectedColorScheme: ColorScheme? {
        switch chosenColorScheme {
        case .light:
            return .light
        case .dark:
            return .dark
        case .system:
            return nil
        }
    }

    var body: some View {
        VStack {
            Picker("chose scheme", selection: $chosenColorScheme) {
                ForEach(ColorSchemeSetting.allCases, id: \.self) {
                    Text($0.rawValue.capitalized)
                }
            }
            .pickerStyle(.segmented)
        }
        .padding()
        .preferredColorScheme(selectedColorScheme)
    }
}

PS do not very well in Preview but works in the Simulator