### 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)

return state->get_bundled_scene();
}
Error PackedScene::pack(Node *p_scene) {
	return state->pack(p_scene);
}
void PackedScene::clear() {
	state->clear();
}
void PackedScene::reload_from_file() {
	String path = get_path();
	if (!path.is_resource_file()) {
		return;
	}
	Ref<PackedScene> s = ResourceLoader::load(ResourceLoader::path_remap(path), get_class(), ResourceFormatLoader::CACHE_MODE_IGNORE);
	if (!s.is_valid()) {
		return;
	}
	
	Ref<SceneState> loaded_state = s->get_state();
	
	
	s->recreate_state();
	
	copy_from(s);
	
	state->copy_from(loaded_state);
}
bool PackedScene::can_instantiate() const {