### Godot version

v4.0.alpha11.official [afdae67cc] (when the feature was added) and newer (still happens in RC6)

### System information

Windows 10

### Issue description

I'm unable to handle when the user sets an exported node property (this feature: https://github.com/godotengine/godot/pull/62185) from a setter in the editor (tool script).

I don't know if this is intentional or not, but for me it was unexpected. I had to revert back to `NodePath`s.

### Steps to reproduce

- Create a scene
- Attach a script to a node
- Add `@tool` at the top of the script
- Export a node property with a setter, preferably with an easy way to see if it executed:
	```
	@export var node:Node:
		set (mod_value):
			prints("node", mod_value)
			node = mod_value
	```
- Save, close and open again the scene to make sure the tool script is running in the editor
- Set the node property from the inspector
- Observe that the setter didn't run

The setter is not bypassed when running the game, it is only bypassed in the editor.

We can compare with a `NodePath` property, which setter is not bypassed regardless if it is in the editor or in game runtime.

### Minimal reproduction project

[nodepath.zip](https://github.com/godotengine/godot/files/10840411/nodepath.zip)

Node *to_node = get_node(p_path);
	if (!Object::cast_to<Viewport>(to_node)) {
		EditorNode::get_singleton()->show_warning(TTR("Selected node is not a Viewport!"));
		return;
	}
	Ref<ViewportTexture> vt;
	vt.instantiate();
	vt->set_viewport_path_in_scene(get_tree()->get_edited_scene_root()->get_path_to(to_node));
	emit_changed(get_edited_property(), vt);
	update_property();
}
void EditorPropertyResource::setup(Object *p_object, const String &p_path, const String &p_base_type) {