### 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_COND_MSG(data.inside_tree && !Thread::is_main_thread(), "Changing the process thread group can only be done from the main thread. Use call_deferred(\"set_process_thread_group\",mode).");
	if (data.process_thread_group == p_mode) {
		return;
	}
	if (!is_inside_tree()) {
		
		data.process_thread_group = p_mode;
		return;
	}
	_remove_tree_from_process_thread_group();
	if (data.process_thread_group != PROCESS_THREAD_GROUP_INHERIT) {
		_remove_process_group();
	}
	data.process_thread_group = p_mode;
	if (p_mode == PROCESS_THREAD_GROUP_INHERIT) {
		if (data.parent) {
			data.process_thread_group_owner = data.parent->data.process_thread_group_owner;
		} else {
			data.process_thread_group_owner = nullptr;
		}
	} else {
		data.process_thread_group_owner = this;
		_add_process_group();
	}
	_add_tree_to_process_thread_group(data.process_thread_group_owner);
	notify_property_list_changed();
}
Node::ProcessThreadGroup Node::get_process_thread_group() const {