### 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)

hbox->add_child(remove_btn);
			}
			prop->update_property();
		}
		if (reorder_to_index % page_length > 0) {
			property_vbox->move_child(property_vbox->get_child(0), reorder_to_index % page_length);
		}
		updating = false;
	} else {
		if (container) {
			set_bottom_editor(nullptr);
			memdelete(container);
			button_add_item = nullptr;
			container = nullptr;
		}
	}
}
void EditorPropertyArray::_remove_pressed(int p_index) {
	Variant array = object->get_array().duplicate();
	array.call("remove_at", p_index);
	emit_changed(get_edited_property(), array, "", false);
	update_property();
}
void EditorPropertyArray::_button_draw() {
	if (dropping) {
		Color color = get_theme_color(SNAME("accent_color"), SNAME("Editor"));
		edit->draw_rect(Rect2(Point2(), edit->get_size()), color, false);
	}
}
bool EditorPropertyArray::_is_drop_valid(const Dictionary &p_drag_data) const {