How to display the AirPlay Menu SwiftUI

Thanks to the airplay audio systemName emoji I made a nice icon

Button(action: {
        showAirplay()
}, label: {
    Image(systemName: "airplayaudio")
        .imageScale(.large)
})

func showAirplay() {
       ???
}

But I have no idea how to display the famous menu :

Finally I managed to solve it myself :D Like said in the comment I have to "embed it inside" UIKit and use it in SwiftUI

Firstly :

struct AirPlayButton: UIViewControllerRepresentable {
    func makeUIViewController(context: UIViewControllerRepresentableContext<AirPlayButton>) -> UIViewController {
        return AirPLayViewController()
    }

    func updateUIViewController(_ uiViewController: UIViewController, context: UIViewControllerRepresentableContext<AirPlayButton>) {

    }
}

Then classic ViewController where we know from ages how to show this famous AirPlay menu popup :

class AirPLayViewController: UIViewController {

    override func viewDidLoad() {
        super.viewDidLoad()
        let isDarkMode = self.traitCollection.userInterfaceStyle == .dark

        let button = UIButton()
        let boldConfig = UIImage.SymbolConfiguration(scale: .large)
        let boldSearch = UIImage(systemName: "airplayaudio", withConfiguration: boldConfig)

        button.setImage(boldSearch, for: .normal)
        button.frame = CGRect(x: 0, y: 0, width: 40, height: 40)
        button.backgroundColor = .red
        button.tintColor = isDarkMode ? .white : .black

        button.addTarget(self, action: #selector(self.showAirPlayMenu(_:)), for: .touchUpInside)
        self.view.addSubview(button)
    }

    @objc func showAirPlayMenu(_ sender: UIButton){ // copied from https://stackoverflow.com/a/44909445/7974174
        let rect = CGRect(x: 0, y: 0, width: 0, height: 0)
        let airplayVolume = MPVolumeView(frame: rect)
        airplayVolume.showsVolumeSlider = false
        self.view.addSubview(airplayVolume)
        for view: UIView in airplayVolume.subviews {
            if let button = view as? UIButton {
                button.sendActions(for: .touchUpInside)
                break
            }
        }
        airplayVolume.removeFromSuperview()
    }
}

Finally in SwiftUI simply call :

struct ContentView: View {
    var body: some View {
        VStack {
            Text("Hello World")
            AirPlayButton().frame(width: 40, height: 40) // (important to be consistent with this frame, like that it is nicely centered... see button.frame in AirPlayViewController)

        }
    }
}