### 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_mode;
}
void Node::_propagate_process_owner(Node *p_owner, int p_pause_notification, int p_enabled_notification) {
	data.process_owner = p_owner;
	if (p_pause_notification != 0) {
		notification(p_pause_notification);
	}
	if (p_enabled_notification != 0) {
		notification(p_enabled_notification);
	}
	data.blocked++;
	for (KeyValue<StringName, Node *> &K : data.children) {
		Node *c = K.value;
		if (c->data.process_mode == PROCESS_MODE_INHERIT) {
			c->_propagate_process_owner(p_owner, p_pause_notification, p_enabled_notification);
		}
	}
	data.blocked--;
}
void Node::set_multiplayer_authority(int p_peer_id, bool p_recursive) {