public Table GetTable()

public async Task ObtainingGeodatabaseFromFeatureLayer()
{
  IEnumerable<Layer> layers = MapView.Active.Map.Layers.Where(layer => layer is FeatureLayer);

  await ArcGIS.Desktop.Framework.Threading.Tasks.QueuedTask.Run(() =>
  {
    foreach (FeatureLayer featureLayer in layers)
    {
      using (Table table = featureLayer.GetTable())
      using (Datastore datastore = table.GetDatastore())
      {
        if (datastore is UnknownDatastore)
          continue;

        Geodatabase geodatabase = datastore as Geodatabase;
      }
    }
  });
}

//Note: call within QueuedTask.Run()
var table = featureLayer.GetTable();
var count = table.GetCount();

await QueuedTask.Run(() =>
{
    using (var table = annoLayer.GetTable())
    {
        using (var rc = table.Search())
        {
            rc.MoveNext();
            using (var af = rc.Current as AnnotationFeature)
            {
                var graphic = af.GetGraphic();
                var textGraphic = graphic as CIMTextGraphic;

                //Note: 
                //var outline_geom = af.GetGraphicOutline(); 
                //gets the anno text outline geometry...
            }
        }
    }
});