public Uri URL {get;}

{
  await QueuedTask.Run(() =>
  {
    Layer selectedLayer = MapView.Active.GetSelectedLayers()[0];

    if (selectedLayer is FeatureLayer)
    {
      FeatureLayer featureLayer = selectedLayer as FeatureLayer;

      using (Table table = featureLayer.GetTable())
      using (Datastore datastore = table.GetDatastore())
      {
        ServiceConnectionProperties serviceConnectionProperties = datastore.GetConnector() as ServiceConnectionProperties;

        if (serviceConnectionProperties == null)
          return;

        Uri url = serviceConnectionProperties.URL;      // Will be the URL to the Feature Service.
        string user = serviceConnectionProperties.User;     // The username property will only be
                                                            // populated for feature service hosted
                                                            // on non-federated ArcGIS Server.
        string password = serviceConnectionProperties.Password; // Will always be empty.
      }
    }
  });
}

{
    //Connect to the AGS service. Note: the connection will persist for the
    //duration of the Pro session.
    var serverUrl = "https://sampleserver6.arcgisonline.com/arcgis/rest/services";

    var username = "user1";
    var password = "user1";

    //at any point before creating a layer, first make a connection to the server
    //if one has not been already established for the current session
    var uri = new Uri(serverUrl);
    var props = new ServiceConnectionProperties(uri)
    {
        User = username
    };
    //It is preferred that you use the Windows Credential Manager to store the password

    //However, it can be set as clear text if you so choose
    props.Password = password; //not recommended


    //Establish a connection to the server at any point in time _before_
    //creating a layer from a service on the server
    //Note: Needs QueuedTask to run
    var gdb = new Geodatabase(props);
    gdb.Dispose();//you do not need the geodatabase object after you have connected.

    //later in the session, as needed...create a layer from one of the services
    //on the server
    var serviceUrl = "https://sampleserver6.arcgisonline.com/arcgis/rest/services/Wildfire_secure/MapServer";
    var lc = new LayerCreationParams(new Uri(serviceUrl));
    //Note: Needs QueuedTask to run
    LayerFactory.Instance.CreateLayer<MapImageLayer>(lc, map);
}