### 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)

Button *button = Object::cast_to<Button>(p_button);
	changing_type_index = p_index;
	Rect2 rect = button->get_screen_rect();
	change_type->reset_size();
	change_type->set_position(rect.get_end() - Vector2(change_type->get_contents_minimum_size().x, 0));
	change_type->popup();
}
void EditorPropertyArray::_change_type_menu(int p_index) {
	if (p_index == Variant::VARIANT_MAX) {
		_remove_pressed(changing_type_index);
		return;
	}
	Variant value;
	VariantInternal::initialize(&value, Variant::Type(p_index));
	Variant array = object->get_array().duplicate();
	array.set(changing_type_index, value);
	emit_changed(get_edited_property(), array, "", true);
	update_property();
}
void EditorPropertyArray::_object_id_selected(const StringName &p_property, ObjectID p_id) {