### 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 data.parent;
}
Node *Node::find_parent(const String &p_pattern) const {
	ERR_THREAD_GUARD_V(nullptr);
	Node *p = data.parent;
	while (p) {
		if (p->data.name.operator String().match(p_pattern)) {
			return p;
		}
		p = p->data.parent;
	}
	return nullptr;
}
Window *Node::get_window() const {
	ERR_THREAD_GUARD_V(nullptr);
	Viewport *vp = get_viewport();
	if (vp) {
		return vp->get_base_window();
	}
	return nullptr;
}
Window *Node::get_last_exclusive_window() const {
	Window *w = get_window();
	while (w && w->get_exclusive_child()) {
		w = w->get_exclusive_child();
	}
	return w;
}
bool Node::is_ancestor_of(const Node *p_node) const {