### 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_event->get_device() != InputEvent::DEVICE_ID_INTERNAL) {
		GDVIRTUAL_CALL(_shortcut_input, p_event);
	}
	if (!is_inside_tree() || !get_viewport() || get_viewport()->is_input_handled()) {
		return;
	}
	shortcut_input(p_event);
}
void Node::_call_unhandled_input(const Ref<InputEvent> &p_event) {
	if (p_event->get_device() != InputEvent::DEVICE_ID_INTERNAL) {
		GDVIRTUAL_CALL(_unhandled_input, p_event);
	}
	if (!is_inside_tree() || !get_viewport() || get_viewport()->is_input_handled()) {
		return;
	}
	unhandled_input(p_event);
}
void Node::_call_unhandled_key_input(const Ref<InputEvent> &p_event) {
	if (p_event->get_device() != InputEvent::DEVICE_ID_INTERNAL) {
		GDVIRTUAL_CALL(_unhandled_key_input, p_event);
	}
	if (!is_inside_tree() || !get_viewport() || get_viewport()->is_input_handled()) {
		return;
	}
	unhandled_key_input(p_event);
}
void Node::_validate_property(PropertyInfo &p_property) const {