### 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)

return data.unique_name_in_owner;
}
void Node::set_owner(Node *p_owner) {
	ERR_MAIN_THREAD_GUARD
	if (data.owner) {
		_clean_up_owner();
	}
	ERR_FAIL_COND(p_owner == this);
	if (!p_owner) {
		return;
	}
	Node *check = this->get_parent();
	bool owner_valid = false;
	while (check) {
		if (check == p_owner) {
			owner_valid = true;
			break;
		}
		check = check->data.parent;
	}
	ERR_FAIL_COND_MSG(!owner_valid, "Invalid owner. Owner must be an ancestor in the tree.");
	_set_owner_nocheck(p_owner);
	if (data.unique_name_in_owner) {
		_acquire_unique_name_in_owner();
	}
}
Node *Node::get_owner() const {