Как проверить, дал ли пользователь разрешение использовать камеру?

Можно импортировать платформу AVFoundation и использовать authorizationStatus (для:) метод, показанный ниже и дескриптор соответствующие случаи.

switch AVCaptureDevice.authorizationStatus(for: .video) {
    case .authorized: // The user has previously granted access to the camera.
        self.setupCaptureSession()

    case .notDetermined: // The user has not yet been asked for camera access.
        AVCaptureDevice.requestAccess(for: .video) { granted in
            if granted {
                self.setupCaptureSession()
            }
        }

    case .denied: // The user has previously denied access.
        return
    case .restricted: // The user can't grant access due to restrictions.
        return
}