### 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)

if (this == p_node) {
		return const_cast<Node *>(p_node);
	}
	HashSet<const Node *> visited;
	const Node *n = this;
	while (n) {
		visited.insert(n);
		n = n->data.parent;
	}
	const Node *common_parent = p_node;
	while (common_parent) {
		if (visited.has(common_parent)) {
			break;
		}
		common_parent = common_parent->data.parent;
	}
	if (!common_parent) {
		return nullptr;
	}
	return const_cast<Node *>(common_parent);
}
NodePath Node::get_path_to(const Node *p_node, bool p_use_unique_path) const {