public class BrowseProjectFilter 

var openDlg = new OpenItemDialog
{
  Title = "Select a Feature Class",
  InitialLocation = @"C:\Data",
  MultiSelect = false,
  BrowseFilter = BrowseProjectFilter.GetFilter(ArcGIS.Desktop.Catalog.ItemFilters.GeodatabaseItems_All)
};

//show the browse dialog
bool? ok = openDlg.ShowDialog();
if (!ok.HasValue || openDlg.Items.Count() == 0)
  return;   //nothing selected

await QueuedTask.Run(() =>
{
  // get the item
  var item = openDlg.Items.First();

  // see if the item has a dataset
  if (ItemFactory.Instance.CanGetDataset(item))
  {
    // get it
    using (var ds = ItemFactory.Instance.GetDataset(item))
    {
      // access some properties
      var name = ds.GetName();
      var path = ds.GetPath();

      // if it's a featureclass
      if (ds is ArcGIS.Core.Data.FeatureClass fc)
      {
        // create a layer 
        var featureLayerParams = new FeatureLayerCreationParams(fc)
        {
          MapMemberIndex = 0
        };
        var layer = LayerFactory.Instance.CreateLayer<FeatureLayer>(featureLayerParams, MapView.Active.Map);

        // continue
      }
    }
  }
});