### 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.process_thread_group;
}
void Node::set_process_thread_messages(BitField<ProcessThreadMessages> p_flags) {
	ERR_THREAD_GUARD
	if (data.process_thread_messages == p_flags) {
		return;
	}
	data.process_thread_messages = p_flags;
}
BitField<Node::ProcessThreadMessages> Node::get_process_thread_messages() const {
	return data.process_thread_messages;
}
void Node::set_process_input(bool p_enable) {
	ERR_THREAD_GUARD
	if (p_enable == data.input) {
		return;
	}
	data.input = p_enable;
	if (!is_inside_tree()) {
		return;
	}
	if (p_enable) {
		add_to_group("_vp_input" + itos(get_viewport()->get_instance_id()));
	} else {
		remove_from_group("_vp_input" + itos(get_viewport()->get_instance_id()));
	}
}
bool Node::is_processing_input() const {