First of all, this way it solved the problem BUT made me think why would I need another ControlTemplate, EditTextScrollbar, when I've set the ScrollBar's DefaultStyle globally in App.cs, all that I need is set the Margin of the ScrollBar inside TextBox. So I've tried, without the, EditTextScrollbar, ControlTemplate, this way:
inputBox.VerticalScrollBarVisibility = ScrollBarVisibility.Auto;
inputBox.Resources.Add(typeof(ScrollBar), new Style() {
Setters = {
//new Setter(ScrollBar.TemplateProperty, new VScrollTemplate()),
new Setter(MarginProperty, new Thickness(0,20,-26,0))
}
})
and it looks like this:

So it doesn't get the DefaultStyle. I've to uncomment new Setter(ScrollBar.TemplateProperty, new VScrollTemplate()) to make it pickup the style, why? Is there anything left to apply the DefaultStyle of ScrollBar?