public string Password {get; set;}

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";

await QueuedTask.Run(() =>
{
  //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
          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 map = MapView.Active.Map;

      QueuedTask.Run(() =>
      {
          var lc = new LayerCreationParams(new Uri(serviceUrl));
          LayerFactory.Instance.CreateLayer<MapImageLayer>(lc, map);
      });