### 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)

n = p_node;
		while (n != common_parent) {
			path.push_back(n->get_name());
			n = n->data.parent;
		}
		n = this;
		while (n != common_parent) {
			path.push_back(up);
			n = n->data.parent;
		}
	}
	path.reverse();
	return NodePath(path, false);
}
NodePath Node::get_path() const {
	ERR_FAIL_COND_V_MSG(!is_inside_tree(), NodePath(), "Cannot get path of node as it is not in a scene tree.");
	if (data.path_cache) {
		return *data.path_cache;
	}
	const Node *n = this;
	Vector<StringName> path;
	while (n) {
		path.push_back(n->get_name());
		n = n->data.parent;
	}
	path.reverse();
	data.path_cache = memnew(NodePath(path, true));
	return *data.path_cache;
}
bool Node::is_in_group(const StringName &p_identifier) const {