### 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_NULL(data.owner); 
	StringName key = StringName(UNIQUE_NODE_PREFIX + data.name.operator String());
	Node **which = data.owner->data.owned_unique_nodes.getptr(key);
	if (which != nullptr && *which != this) {
		String which_path = is_inside_tree() ? (*which)->get_path() : data.owner->get_path_to(*which);
		WARN_PRINT(vformat("Setting node name '%s' to be unique within scene for '%s', but it's already claimed by '%s'.\n'%s' is no longer set as having a unique name.",
				get_name(), is_inside_tree() ? get_path() : data.owner->get_path_to(this), which_path, which_path));
		data.unique_name_in_owner = false;
		return;
	}
	data.owner->data.owned_unique_nodes[key] = this;
}
void Node::set_unique_name_in_owner(bool p_enabled) {
	ERR_MAIN_THREAD_GUARD
	if (data.unique_name_in_owner == p_enabled) {
		return;
	}
	if (data.unique_name_in_owner && data.owner != nullptr) {
		_release_unique_name_in_owner();
	}
	data.unique_name_in_owner = p_enabled;
	if (data.unique_name_in_owner && data.owner != nullptr) {
		_acquire_unique_name_in_owner();
	}
	update_configuration_warnings();
}
bool Node::is_unique_name_in_owner() const {