### 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 (data.owner) {
		bool found = false;
		Node *parent = data.parent;
		while (parent) {
			if (parent == data.owner) {
				found = true;
				break;
			}
			parent = parent->data.parent;
		}
		if (!found) {
			_clean_up_owner();
		}
	}
	data.blocked++;
	for (HashMap<StringName, Node *>::Iterator I = data.children.last(); I; --I) {
		I->value->_propagate_after_exit_tree();
	}
	data.blocked--;
	emit_signal(SceneStringNames::get_singleton()->tree_exited);
}
void Node::_propagate_exit_tree() {