### 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)

print_line(_get_tree_string_pretty("", true));
}
void Node::print_tree() {
	print_line(_get_tree_string(this));
}
String Node::_get_tree_string_pretty(const String &p_prefix, bool p_last) {
	String new_prefix = p_last ? String::utf8(" ┖╴") : String::utf8(" ┠╴");
	_update_children_cache();
	String return_tree = p_prefix + new_prefix + String(get_name()) + "\n";
	for (uint32_t i = 0; i < data.children_cache.size(); i++) {
		new_prefix = p_last ? String::utf8("   ") : String::utf8(" ┃ ");
		return_tree += data.children_cache[i]->_get_tree_string_pretty(p_prefix + new_prefix, i == data.children_cache.size() - 1);
	}
	return return_tree;
}
String Node::get_tree_string_pretty() {
	return _get_tree_string_pretty("", true);
}
String Node::_get_tree_string(const Node *p_node) {
	_update_children_cache();
	String return_tree = String(p_node->get_path_to(this)) + "\n";
	for (uint32_t i = 0; i < data.children_cache.size(); i++) {
		return_tree += data.children_cache[i]->_get_tree_string(p_node);
	}
	return return_tree;
}
String Node::get_tree_string() {