### 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(idx != -1, false);
	n = p_node;
	idx = p_node->data.depth - 1;
	while (n) {
		ERR_FAIL_INDEX_V(idx, p_node->data.depth, false);
		that_stack[idx--] = n->get_index();
		n = n->data.parent;
	}
	ERR_FAIL_COND_V(idx != -1, false);
	idx = 0;
	bool res;
	while (true) {
		
		int this_idx = (idx >= data.depth) ? -2 : this_stack[idx];
		int that_idx = (idx >= p_node->data.depth) ? -2 : that_stack[idx];
		if (this_idx > that_idx) {
			res = true;
			break;
		} else if (this_idx < that_idx) {
			res = false;
			break;
		} else if (this_idx == -2) {
			res = false; 
			break;
		}
		idx++;
	}
	return res;
}
void Node::get_owned_by(Node *p_by, List<Node *> *p_owned) {