### 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)

ERR_FAIL_COND_V(!is_inside_tree(), ERR_UNCONFIGURED);
	Ref<MultiplayerAPI> api = get_multiplayer();
	if (api.is_null()) {
		return ERR_UNCONFIGURED;
	}
	return api->rpcp(this, p_peer_id, p_method, p_arg, p_argcount);
}
Ref<MultiplayerAPI> Node::get_multiplayer() const {
	if (!is_inside_tree()) {
		return Ref<MultiplayerAPI>();
	}
	return get_tree()->get_multiplayer(get_path());
}
bool Node::can_process_notification(int p_what) const {
	switch (p_what) {
		case NOTIFICATION_PHYSICS_PROCESS:
			return data.physics_process;
		case NOTIFICATION_PROCESS:
			return data.process;
		case NOTIFICATION_INTERNAL_PROCESS:
			return data.process_internal;
		case NOTIFICATION_INTERNAL_PHYSICS_PROCESS:
			return data.physics_process_internal;
	}
	return true;
}
bool Node::can_process() const {