### 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_THREAD_GUARD_V(nullptr);
	Node *node = get_node(p_path);
	r_res = Ref<Resource>();
	r_leftover_subpath = Vector<StringName>();
	if (!node) {
		return nullptr;
	}
	if (p_path.get_subname_count()) {
		int j = 0;
		// If not p_last_is_property, we shouldn't consider the last one as part of the resource
		for (; j < p_path.get_subname_count() - (int)p_last_is_property; j++) {
			bool is_valid = false;
			Variant new_res_v = j == 0 ? node->get(p_path.get_subname(j), &is_valid) : r_res->get(p_path.get_subname(j), &is_valid);
			if (!is_valid) { // Found nothing on that path
				return nullptr;
			}
			Ref<Resource> new_res = new_res_v;
			if (new_res.is_null()) { // No longer a resource, assume property
				break;
			}
			r_res = new_res;
		}
		for (; j < p_path.get_subname_count(); j++) {
			// Put the rest of the subpath in the leftover path
			r_leftover_subpath.push_back(p_path.get_subname(j));
		}
	}
	return node;
}
void Node::_set_tree(SceneTree *p_tree) {