Capturing a picture in SwiftUI by showing a sheet

Question

Goal: To capture an image and provide it to a parent view via a binding to display it in the UI.

My code:

struct ImageShooter: UIViewControllerRepresentable {
    @Binding var image: UIImage?
    var captureSesssion = AVCaptureSession()
    var output = AVCapturePhotoOutput()
    
    func makeUIViewController(context: Context) -> UIViewController {
        let camera = AVCaptureDevice.default(for: .video)
        let input = try! AVCaptureDeviceInput(device: camera!)
        captureSesssion.addInput(input)
        captureSesssion.addOutput(output)
        let preview = AVCaptureVideoPreviewLayer(session: captureSesssion)
        preview.videoGravity = .resizeAspectFill
        let vc = UIViewController()
        vc.view.layer.addSublayer(preview)
        preview.frame = vc.view.frame
        return vc
    }

    func updateUIViewController(_ uiViewController: UIViewController, context: Context) {

    }
    
    func makeCoordinator() -> Coordinator {
        Coordinator(self)
    }
    
    class Coordinator: NSObject, AVCapturePhotoCaptureDelegate {
        var parent: ImageShooter
        
        init(_ parent: ImageShooter) {
            self.parent = parent
        }

        func photoOutput(_ output: AVCapturePhotoOutput, didFinishProcessingPhoto photo: AVCapturePhoto, error: Error?) {
            if let imageData = photo.fileDataRepresentation() {
                guard let image = UIImage(data: imageData) else { return }
                self.parent.image = image
            }
        }

        func photoOutput(_ output: AVCapturePhotoOutput, didFinishCaptureFor resolvedSettings: AVCaptureResolvedPhotoSettings, error: Error?) {
            parent.output = output
            parent.captureSesssion.stopRunning()
        }
    }
}

Problem: The screen remains black and no camera preview is shown. The sheet appears. The sheet can be dismissed.