### 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 (!p_node) {
		return false; // Easier, null is never editable. :)
	}
	ERR_FAIL_COND_V(!is_ancestor_of(p_node), false);
	return p_node->data.editable_instance;
}
Node *Node::get_deepest_editable_node(Node *p_start_node) const {
	ERR_THREAD_GUARD_V(nullptr);
	ERR_FAIL_NULL_V(p_start_node, nullptr);
	ERR_FAIL_COND_V(!is_ancestor_of(p_start_node), p_start_node);
	Node const *iterated_item = p_start_node;
	Node *node = p_start_node;
	while (iterated_item->get_owner() && iterated_item->get_owner() != this) {
		if (!is_editable_instance(iterated_item->get_owner())) {
			node = iterated_item->get_owner();
		}
		iterated_item = iterated_item->get_owner();
	}
	return node;
}
#ifdef TOOLS_ENABLED
void Node::set_property_pinned(const String &p_property, bool p_pinned) {