### 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)

switch (p_internal_mode) {
		case INTERNAL_MODE_FRONT: {
			p_child->data.index = data.internal_children_front_count_cache++;
		} break;
		case INTERNAL_MODE_BACK: {
			p_child->data.index = data.internal_children_back_count_cache++;
		} break;
		case INTERNAL_MODE_DISABLED: {
			p_child->data.index = data.external_children_count_cache++;
		} break;
	}
	p_child->data.parent = this;
	if (!data.children_cache_dirty && p_internal_mode == INTERNAL_MODE_DISABLED && data.internal_children_back_count_cache == 0) {
		
		data.children_cache.push_back(p_child);
	} else {
		data.children_cache_dirty = true;
	}
	p_child->notification(NOTIFICATION_PARENTED);
	if (data.tree) {
		p_child->_set_tree(data.tree);
	}
	
	
	p_child->data.parent_owned = data.in_constructor;
	add_child_notify(p_child);
	notification(NOTIFICATION_CHILD_ORDER_CHANGED);
	emit_signal(SNAME("child_order_changed"));
}
void Node::add_child(Node *p_child, bool p_force_readable_name, InternalMode p_internal) {