### 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.path_cache) {
				memdelete(data.path_cache);
				data.path_cache = nullptr;
			}
		} break;
		case NOTIFICATION_PATH_RENAMED: {
			if (data.path_cache) {
				memdelete(data.path_cache);
				data.path_cache = nullptr;
			}
		} break;
		case NOTIFICATION_READY: {
			if (GDVIRTUAL_IS_OVERRIDDEN(_input)) {
				set_process_input(true);
			}
			if (GDVIRTUAL_IS_OVERRIDDEN(_shortcut_input)) {
				set_process_shortcut_input(true);
			}
			if (GDVIRTUAL_IS_OVERRIDDEN(_unhandled_input)) {
				set_process_unhandled_input(true);
			}
			if (GDVIRTUAL_IS_OVERRIDDEN(_unhandled_key_input)) {
				set_process_unhandled_key_input(true);
			}
			if (GDVIRTUAL_IS_OVERRIDDEN(_process)) {
				set_process(true);
			}
			if (GDVIRTUAL_IS_OVERRIDDEN(_physics_process)) {
				set_physics_process(true);
			}