public void Modify( 
   Table table,
   long oid,
   string fieldName,
   object value
)

//See "Change Annotation Text Graphic" for an alternative if TEXTSTRING is missing from the schema
await QueuedTask.Run(() =>
{
    //annoLayer is ~your~ Annotation layer...

    // use the inspector methodology
    var insp = new Inspector();
    insp.Load(annoLayer, oid);

    // make sure TextString attribute exists.
    //It is not guaranteed to be in the schema
    ArcGIS.Desktop.Editing.Attributes.Attribute att = insp.FirstOrDefault(a => a.FieldName == "TEXTSTRING");
    if (att != null)
    {
        insp["TEXTSTRING"] = "Hello World";

        //create and execute the edit operation
        EditOperation op = new EditOperation();
        op.Name = "Update annotation";
        op.Modify(insp);

        //OR using a Dictionary - again TEXTSTRING has to exist in the schema
        //Dictionary<string, object> newAtts = new Dictionary<string, object>();
        //newAtts.Add("TEXTSTRING", "hello world");
        //op.Modify(annoLayer, oid, newAtts);

        op.Execute();
    }
});

//must support editing!
var featSceneLayer = MapView.Active.Map.GetLayersAsFlattenedList()
                   .OfType<FeatureSceneLayer>().FirstOrDefault();
if (!featSceneLayer.HasAssociatedFeatureService || 
    !featSceneLayer.IsEditable)
  return;

var ok = await QueuedTask.Run(() =>
{
  var editOp = new EditOperation()
  {
    Name = "Edit FeatureSceneLayer Attributes",
    SelectModifiedFeatures = true
  };
  //make an inspector
  var inspector = new Inspector();
  //get the attributes for the specified oid
  inspector.Load(featSceneLayer, oid);
  inspector["PermitNotes"] = "test";//modify
  editOp.Modify(inspector);
  return editOp.Execute();//synchronous flavor
});