### 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)

}
	data.blocked++;
	
	for (int i = motion_from; i <= motion_to; i++) {
		if (data.children_cache[i]->data.internal_mode == INTERNAL_MODE_DISABLED) {
			data.children_cache[i]->data.index = i - data.internal_children_front_count_cache;
		} else if (data.children_cache[i]->data.internal_mode == INTERNAL_MODE_BACK) {
			data.children_cache[i]->data.index = i - data.internal_children_front_count_cache - data.external_children_count_cache;
		} else {
			data.children_cache[i]->data.index = i;
		}
	}
	
	move_child_notify(p_child);
	notification(NOTIFICATION_CHILD_ORDER_CHANGED);
	emit_signal(SNAME("child_order_changed"));
	p_child->_propagate_groups_dirty();
	data.blocked--;
}
void Node::_propagate_groups_dirty() {
	for (const KeyValue<StringName, GroupData> &E : data.grouped) {
		if (E.value.group) {
			E.value.group->changed = true;
		}
	}
	for (KeyValue<StringName, Node *> &K : data.children) {
		K.value->_propagate_groups_dirty();
	}
}
void Node::add_child_notify(Node *p_child) {