A string data is attached during DragInit event by using following code.

public StoreDataObjectUsingEventHandler()
{
    InitializeComponent();
    ISEventManager.RegisterInstanceHandler(
        UXListBox1, // any element in the routed path which applicable in your scenario
        ISDragDrop.DragSourceEvent, // the routed event
        new DragEventHandler(UXListBox1_DragInit), // the event handler
        true);
}
private void UXListBox1_DragInit(object sender, DragEventArgs e)
{
    string sourceData = "Some string data to store...";
    byte[] unicodeText = Encoding.Unicode.GetBytes(sourceData);
    byte[] utf8Text = Encoding.UTF8.GetBytes(sourceData);
    string uniCodeFormat = "Unicode";
    string utf8DataFormat = "UTF-8";
    var dataObject = e.Data as DragDropEventData;
    dataObject.SetData(sourceData);
    dataObject.SetData(uniCodeFormat, unicodeText);
    dataObject.SetData(utf8DataFormat, utf8Text);
}

The data could then be retrieved in PrepareDrop event by invoking GetData() method.

public StoreDataObjectUsingEventHandler()
{
    InitializeComponent();
    ...
            
    ISEventManager.RegisterInstanceHandler(
        UXListBox2,
        ISDragDrop.PrepareDropEvent,
        new DragEventHandler(UXListBox2_PrepareDrop),
        true);
}
private void UXListBox2_PrepareDrop(object sender, DragEventArgs e)
{
    var dataObject = e.Data as DragDropEventData;
            
    if (dataObject != null)
    {
        string retrievedData = dataObject.GetData().ToString();
    }
}

Hope this helps.