public string Expression {get; set;}

{
  // Note: the following should be embedded in a QueuedTask.Run() statement
  {
    //Get the layer's definition, using the community sample Data\Admin\AdminSample.aprx
    if (featureLayer.GetDefinition() is not CIMFeatureLayer lyrDefn)
    {
      // not a feature layer, leave
      return;
    }
    //Get the label classes - we need the first one
    var listLabelClasses = lyrDefn.LabelClasses.ToList();
    var theLabelClass = listLabelClasses.FirstOrDefault();
    //set the label class Expression to use the Arcade expression
    theLabelClass.Expression = "return $feature.STATE_NAME + TextFormatting.NewLine + $feature.POP2000;";
    //Set the label definition back to the layer.
    featureLayer.SetDefinition(lyrDefn);
  }
}