public void SelectLayers( 
   IReadOnlyCollection<Layer> layers
)

{
  //Zoom to the selected layers in the TOC
  var featureLayers = mapView.Map.Layers.OfType<FeatureLayer>();
  mapView.SelectLayers(featureLayers.ToList());
}

{
  // select it in the TOC
  List<Layer> layersToSelect = [featureLayer];
  MapView.Active.SelectLayers(layersToSelect);

  // now execute the layer properties command
  var wrapper = FrameworkApplication.GetPlugInWrapper("esri_mapping_selectedLayerPropertiesButton");
  var command = wrapper as ICommand;
  if (command == null)
  {
    // the command is not found, leave
  }

  // execute the command
  if (command.CanExecute(null))
    command.Execute(null);
}