### 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)

void _resource_changed(const Ref<Resource> &p_resource);
	void _viewport_selected(const NodePath &p_path);
	void _sub_inspector_property_keyed(const String &p_property, const Variant &p_value, bool p_advance);
	void _sub_inspector_resource_selected(const Ref<Resource> &p_resource, const String &p_property);
	void _sub_inspector_object_id_selected(int p_id);
	void _open_editor_pressed();
	void _update_property_bg();
	void _update_preferred_shader();
protected:
	virtual void _set_read_only(bool p_read_only) override;
	void _notification(int p_what);
public:
	virtual void update_property() override;
	void setup(Object *p_object, const String &p_path, const String &p_base_type);
	void collapse_all_folding() override;
	void expand_all_folding() override;
	void expand_revertable() override;
	void set_use_sub_inspector(bool p_enable);
	void fold_resource();
	EditorPropertyResource();
};
class EditorInspectorDefaultPlugin : public EditorInspectorPlugin {
	GDCLASS(EditorInspectorDefaultPlugin, EditorInspectorPlugin);
public:
	virtual bool can_handle(Object *p_object) override;
	virtual bool parse_property(Object *p_object, const Variant::Type p_type, const String &p_path, const PropertyHint p_hint, const String &p_hint_text, const BitField<PropertyUsageFlags> p_usage, const bool p_wide = false) override;
	static EditorProperty *get_editor_for_property(Object *p_object, const Variant::Type p_type, const String &p_path, const PropertyHint p_hint, const String &p_hint_text, const BitField<PropertyUsageFlags> p_usage, const bool p_wide = false);
};
#endif