### Godot version

v4.2.dev.custom_build [0ca854232]

### System information

Pop Os 22.04 lts 12th Gen Intel® Core™ i7-12700H × 20 NVIDIA RTX A2000 8GB 32.0GB  ram

### Issue description

A node that has a script attached to it and it has a couple of child nodes (type of a child node doesn't matter). In the script you have an export variable of type Node. You save the scene into a file and you add it in level scene. When you start to duplicate that scene in the level and you'll hover over exported variable to show a node path, it will show an incorrect path. 


https://github.com/godotengine/godot/assets/33091666/75088d1b-c014-41e0-bae3-46610eccbad1



### Steps to reproduce

1. create a scene with a node and a child node.
2. attach a script to the parent node and create an export variable of type Node
3. assign child node to that exported variable through the editor
4. save the scene and create a level scene where you are going to add just saved scene.
5. _Possibly requires a reboot of the engine before seeing the bug_
6. start duplicating nodes in the level scene

### Minimal reproduction project

[NodeTest.zip](https://github.com/godotengine/godot/files/12781547/NodeTest.zip)

return p_property;
}
bool Node::is_part_of_edited_scene() const {
	return Engine::get_singleton()->is_editor_hint() && is_inside_tree() && get_tree()->get_edited_scene_root() &&
			(get_tree()->get_edited_scene_root() == this || get_tree()->get_edited_scene_root()->is_ancestor_of(this));
}
#endif
void Node::get_storable_properties(HashSet<StringName> &r_storable_properties) const {
	ERR_THREAD_GUARD
	List<PropertyInfo> pi;
	get_property_list(&pi);
	for (List<PropertyInfo>::Element *E = pi.front(); E; E = E->next()) {
		if ((E->get().usage & PROPERTY_USAGE_STORAGE)) {
			r_storable_properties.insert(E->get().name);
		}
	}
}
String Node::to_string() {
	ERR_THREAD_GUARD_V(String());
	if (get_script_instance()) {
		bool valid;
		String ret = get_script_instance()->to_string(&valid);
		if (valid) {
			return ret;
		}
	}
	return (get_name() ? String(get_name()) + ":" : "") + Object::to_string();
}
void Node::set_scene_instance_state(const Ref<SceneState> &p_state) {