public sealed class GDBProjectItem : ArcGIS.Desktop.Internal.Catalog.ProjectItemInfoCrawl, ArcGIS.Desktop.Core.IMetadata, ArcGIS.Desktop.Core.IProjectItem, System.ComponentModel.INotifyPropertyChanged  

/// Add a file geodatabase or a SQLite or enterprise database connection to a project
Item gdbToAdd = folderToAdd.GetItems().FirstOrDefault(folderItem => folderItem.Name.Equals("CountyData.gdb"));
var addedGeodatabase = await QueuedTask.Run(() => Project.Current.AddItem(gdbToAdd as IProjectItem));

IEnumerable<GDBProjectItem> newGDBItemsContainer = null;
newGDBItemsContainer = Project.Current.GetItems<GDBProjectItem>();
foreach (var GDBItem in newGDBItemsContainer)
{
  //Do Something with the GDB.
}

GDBProjectItem GDBProjItem = Project.Current.GetItems<GDBProjectItem>().FirstOrDefault(item => item.Name.Equals("myGDB"));

public async Task ObtainingGeodatabaseFromProjectItem()
{
  IEnumerable<GDBProjectItem> gdbProjectItems = Project.Current.GetItems<GDBProjectItem>();

  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    foreach (GDBProjectItem gdbProjectItem in gdbProjectItems)
    {
      using (Datastore datastore = gdbProjectItem.GetDatastore())
      {
        //Unsupported datastores (non File GDB and non Enterprise GDB) will be of type UnknownDatastore
        if (datastore is UnknownDatastore)
          continue;

        Geodatabase geodatabase = datastore as Geodatabase;
        // Use the geodatabase.
      }
    }
  });
}