### 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)

}
	}
	for (int i = 0; i < p_node->get_child_count(); i++) {
		Node *c = p_node->get_child(i);
		Error err = _parse_connections(p_owner, c, name_map, variant_map, node_map, nodepath_map);
		if (err) {
			return err;
		}
	}
	return OK;
}
Error SceneState::pack(Node *p_scene) {
	ERR_FAIL_NULL_V(p_scene, ERR_INVALID_PARAMETER);
	clear();
	Node *scene = p_scene;
	HashMap<StringName, int> name_map;
	HashMap<Variant, int, VariantHasher, VariantComparator> variant_map;
	HashMap<Node *, int> node_map;
	HashMap<Node *, int> nodepath_map;
	
	if (scene->get_scene_inherited_state().is_valid()) {
		String scene_path = scene->get_scene_inherited_state()->get_path();
		Ref<PackedScene> instance = ResourceLoader::load(scene_path);
		if (instance.is_valid()) {
			base_scene_idx = _vm_get_variant(instance, variant_map);
		}
	}
	
	Error err = _parse_node(scene, scene, -1, name_map, variant_map, node_map, nodepath_map);
	if (err) {