### 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.process_thread_group == PROCESS_THREAD_GROUP_INHERIT) {
					if (data.parent) {
						data.process_thread_group_owner = data.parent->data.process_thread_group_owner;
					}
					if (data.process_thread_group_owner) {
						data.process_group = data.process_thread_group_owner->data.process_group;
					} else {
						data.process_group = &data.tree->default_process_group;
					}
				} else {
					data.process_thread_group_owner = this;
					_add_process_group();
				}
				if (_is_any_processing()) {
					_add_to_process_thread_group();
				}
			}
			if (data.input) {
				add_to_group("_vp_input" + itos(get_viewport()->get_instance_id()));
			}
			if (data.shortcut_input) {
				add_to_group("_vp_shortcut_input" + itos(get_viewport()->get_instance_id()));
			}
			if (data.unhandled_input) {
				add_to_group("_vp_unhandled_input" + itos(get_viewport()->get_instance_id()));
			}
			if (data.unhandled_key_input) {
				add_to_group("_vp_unhandled_key_input" + itos(get_viewport()->get_instance_id()));
			}