### 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 get_node_or_null(p_path) != nullptr;
}
Node *Node::find_child(const String &p_pattern, bool p_recursive, bool p_owned) const {
	ERR_THREAD_GUARD_V(nullptr);
	ERR_FAIL_COND_V(p_pattern.is_empty(), nullptr);
	_update_children_cache();
	Node *const *cptr = data.children_cache.ptr();
	int ccount = data.children_cache.size();
	for (int i = 0; i < ccount; i++) {
		if (p_owned && !cptr[i]->data.owner) {
			continue;
		}
		if (cptr[i]->data.name.operator String().match(p_pattern)) {
			return cptr[i];
		}
		if (!p_recursive) {
			continue;
		}
		Node *ret = cptr[i]->find_child(p_pattern, true, p_owned);
		if (ret) {
			return ret;
		}
	}
	return nullptr;
}
TypedArray<Node> Node::find_children(const String &p_pattern, const String &p_type, bool p_recursive, bool p_owned) const {