### 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)

ERR_FAIL_COND_MSG(data.inside_tree && !Thread::is_main_thread(), "Adding children to a node inside the SceneTree is only allowed from the main thread. Use call_deferred(\"add_child\",node).");
	ERR_THREAD_GUARD
	ERR_FAIL_NULL(p_child);
	ERR_FAIL_COND_MSG(p_child == this, vformat("Can't add child '%s' to itself.", p_child->get_name())); 
	ERR_FAIL_COND_MSG(p_child->data.parent, vformat("Can't add child '%s' to '%s', already has a parent '%s'.", p_child->get_name(), get_name(), p_child->data.parent->get_name())); 
#ifdef DEBUG_ENABLED
	ERR_FAIL_COND_MSG(p_child->is_ancestor_of(this), vformat("Can't add child '%s' to '%s' as it would result in a cyclic dependency since '%s' is already a parent of '%s'.", p_child->get_name(), get_name(), p_child->get_name(), get_name()));
#endif
	ERR_FAIL_COND_MSG(data.blocked > 0, "Parent node is busy setting up children, `add_child()` failed. Consider using `add_child.call_deferred(child)` instead.");
	_validate_child_name(p_child, p_force_readable_name);
#ifdef DEBUG_ENABLED
	if (p_child->data.owner && !p_child->data.owner->is_ancestor_of(p_child)) {
		
		WARN_PRINT(vformat("Adding '%s' as child to '%s' will make owner '%s' inconsistent. Consider unsetting the owner beforehand.", p_child->get_name(), get_name(), p_child->data.owner->get_name()));
	}
#endif 
	_add_child_nocheck(p_child, p_child->data.name, p_internal);
}
void Node::add_sibling(Node *p_sibling, bool p_force_readable_name) {
	ERR_FAIL_COND_MSG(data.inside_tree && !Thread::is_main_thread(), "Adding a sibling to a node inside the SceneTree is only allowed from the main thread. Use call_deferred(\"add_sibling\",node).");
	ERR_FAIL_NULL(p_sibling);
	ERR_FAIL_COND_MSG(p_sibling == this, vformat("Can't add sibling '%s' to itself.", p_sibling->get_name())); 
	ERR_FAIL_NULL(data.parent);
	ERR_FAIL_COND_MSG(data.parent->data.blocked > 0, "Parent node is busy setting up children, `add_sibling()` failed. Consider using `add_sibling.call_deferred(sibling)` instead.");
	data.parent->add_child(p_sibling, p_force_readable_name, data.internal_mode);
	data.parent->_update_children_cache();
	data.parent->_move_child(p_sibling, get_index() + 1);
}
void Node::remove_child(Node *p_child) {