### 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)

String description;
	if (is_inside_tree()) {
		description = get_path();
	} else {
		description = get_name();
		if (description.is_empty()) {
			description = get_class();
		}
	}
	return description;
}
static SafeRefCount node_hrcr_count;
void Node::init_node_hrcr() {
	node_hrcr_count.init(1);
}
#ifdef TOOLS_ENABLED
String Node::validate_child_name(Node *p_child) {
	StringName name = p_child->data.name;
	_generate_serial_child_name(p_child, name);
	return name;
}
#endif
String Node::adjust_name_casing(const String &p_name) {