### 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)

GEN_EDIT_STATE_DISABLED,
		GEN_EDIT_STATE_INSTANCE,
		GEN_EDIT_STATE_MAIN,
		GEN_EDIT_STATE_MAIN_INHERITED,
	};
	Error pack(Node *p_scene);
	void clear();
	bool can_instantiate() const;
	Node *instantiate(GenEditState p_edit_state = GEN_EDIT_STATE_DISABLED) const;
	void recreate_state();
	void replace_state(Ref<SceneState> p_by);
	virtual void reload_from_file() override;
	virtual void set_path(const String &p_path, bool p_take_over = false) override;
#ifdef TOOLS_ENABLED
	virtual void set_last_modified_time(uint64_t p_time) override {
		state->set_last_modified_time(p_time);
	}
#endif
	Ref<SceneState> get_state() const;
	PackedScene();
};
VARIANT_ENUM_CAST(PackedScene::GenEditState)
#endif