### Godot version

v4.0.alpha11.official [afdae67cc] (when the feature was added) and newer (still happens in RC6)

### System information

Windows 10

### Issue description

I'm unable to handle when the user sets an exported node property (this feature: https://github.com/godotengine/godot/pull/62185) from a setter in the editor (tool script).

I don't know if this is intentional or not, but for me it was unexpected. I had to revert back to `NodePath`s.

### Steps to reproduce

- Create a scene
- Attach a script to a node
- Add `@tool` at the top of the script
- Export a node property with a setter, preferably with an easy way to see if it executed:
	```
	@export var node:Node:
		set (mod_value):
			prints("node", mod_value)
			node = mod_value
	```
- Save, close and open again the scene to make sure the tool script is running in the editor
- Set the node property from the inspector
- Observe that the setter didn't run

The setter is not bypassed when running the game, it is only bypassed in the editor.

We can compare with a `NodePath` property, which setter is not bypassed regardless if it is in the editor or in game runtime.

### Minimal reproduction project

[nodepath.zip](https://github.com/godotengine/godot/files/10840411/nodepath.zip)

nd.index = -1;
	} else {
		
		nd.index = p_node->get_index();
	}
	
	
	
	
	bool instantiated_by_owner = false;
	Vector<SceneState::PackState> states_stack = PropertyUtils::get_node_states_stack(p_node, p_owner, &instantiated_by_owner);
	if (!p_node->get_scene_file_path().is_empty() && p_node->get_owner() == p_owner && instantiated_by_owner) {
		if (p_node->get_scene_instance_load_placeholder()) {
			
			nd.instance = _vm_get_variant(p_node->get_scene_file_path(), variant_map);
			nd.instance |= FLAG_INSTANCE_IS_PLACEHOLDER;
		} else {
			
			Ref<PackedScene> instance = ResourceLoader::load(p_node->get_scene_file_path());
			if (!instance.is_valid()) {
				return ERR_CANT_OPEN;
			}
			nd.instance = _vm_get_variant(instance, variant_map);
		}
	}
	
	
	List<PropertyInfo> plist;
	p_node->get_property_list(&plist);
	Array pinned_props = _sanitize_node_pinned_properties(p_node);