### 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)

ClassDB::bind_method(D_METHOD("move_child", "child_node", "to_index"), &Node::move_child);
	ClassDB::bind_method(D_METHOD("get_groups"), &Node::_get_groups);
	ClassDB::bind_method(D_METHOD("set_owner", "owner"), &Node::set_owner);
	ClassDB::bind_method(D_METHOD("get_owner"), &Node::get_owner);
	ClassDB::bind_method(D_METHOD("get_index", "include_internal"), &Node::get_index, DEFVAL(false));
	ClassDB::bind_method(D_METHOD("print_tree"), &Node::print_tree);
	ClassDB::bind_method(D_METHOD("print_tree_pretty"), &Node::print_tree_pretty);
	ClassDB::bind_method(D_METHOD("get_tree_string"), &Node::get_tree_string);
	ClassDB::bind_method(D_METHOD("get_tree_string_pretty"), &Node::get_tree_string_pretty);
	ClassDB::bind_method(D_METHOD("set_scene_file_path", "scene_file_path"), &Node::set_scene_file_path);
	ClassDB::bind_method(D_METHOD("get_scene_file_path"), &Node::get_scene_file_path);
	ClassDB::bind_method(D_METHOD("propagate_notification", "what"), &Node::propagate_notification);
	ClassDB::bind_method(D_METHOD("propagate_call", "method", "args", "parent_first"), &Node::propagate_call, DEFVAL(Array()), DEFVAL(false));
	ClassDB::bind_method(D_METHOD("set_physics_process", "enable"), &Node::set_physics_process);
	ClassDB::bind_method(D_METHOD("get_physics_process_delta_time"), &Node::get_physics_process_delta_time);
	ClassDB::bind_method(D_METHOD("is_physics_processing"), &Node::is_physics_processing);
	ClassDB::bind_method(D_METHOD("get_process_delta_time"), &Node::get_process_delta_time);
	ClassDB::bind_method(D_METHOD("set_process", "enable"), &Node::set_process);
	ClassDB::bind_method(D_METHOD("set_process_priority", "priority"), &Node::set_process_priority);
	ClassDB::bind_method(D_METHOD("get_process_priority"), &Node::get_process_priority);
	ClassDB::bind_method(D_METHOD("set_physics_process_priority", "priority"), &Node::set_physics_process_priority);
	ClassDB::bind_method(D_METHOD("get_physics_process_priority"), &Node::get_physics_process_priority);
	ClassDB::bind_method(D_METHOD("is_processing"), &Node::is_processing);
	ClassDB::bind_method(D_METHOD("set_process_input", "enable"), &Node::set_process_input);
	ClassDB::bind_method(D_METHOD("is_processing_input"), &Node::is_processing_input);
	ClassDB::bind_method(D_METHOD("set_process_shortcut_input", "enable"), &Node::set_process_shortcut_input);
	ClassDB::bind_method(D_METHOD("is_processing_shortcut_input"), &Node::is_processing_shortcut_input);
	ClassDB::bind_method(D_METHOD("set_process_unhandled_input", "enable"), &Node::set_process_unhandled_input);
	ClassDB::bind_method(D_METHOD("is_processing_unhandled_input"), &Node::is_processing_unhandled_input);
	ClassDB::bind_method(D_METHOD("set_process_unhandled_key_input", "enable"), &Node::set_process_unhandled_key_input);