@giusischiri when clicking on the pinned TaskBar-Icon or in Startmenu you don't start a separate Edge Instance, it is just a new Window of the already started Edge - you can clearly see this e.g. with Process Explorer, it is just an additional child of the already running Edge.
So you would have to configure the NewTabPageLocation to get what you expect. But New Tab then opens with this Location too. I currently see no way to separately configure New Tab and New Window.