### 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;
}
void PackedScene::set_path(const String &p_path, bool p_take_over) {
	state->set_path(p_path);
	Resource::set_path(p_path, p_take_over);
}
void PackedScene::reset_state() {
	clear();
}
void PackedScene::_bind_methods() {
	ClassDB::bind_method(D_METHOD("pack", "path"), &PackedScene::pack);
	ClassDB::bind_method(D_METHOD("instantiate", "edit_state"), &PackedScene::instantiate, DEFVAL(GEN_EDIT_STATE_DISABLED));
	ClassDB::bind_method(D_METHOD("can_instantiate"), &PackedScene::can_instantiate);
	ClassDB::bind_method(D_METHOD("_set_bundled_scene", "scene"), &PackedScene::_set_bundled_scene);
	ClassDB::bind_method(D_METHOD("_get_bundled_scene"), &PackedScene::_get_bundled_scene);
	ClassDB::bind_method(D_METHOD("get_state"), &PackedScene::get_state);
	ADD_PROPERTY(PropertyInfo(Variant::DICTIONARY, "_bundled"), "_set_bundled_scene", "_get_bundled_scene");
	BIND_ENUM_CONSTANT(GEN_EDIT_STATE_DISABLED);
	BIND_ENUM_CONSTANT(GEN_EDIT_STATE_INSTANCE);
	BIND_ENUM_CONSTANT(GEN_EDIT_STATE_MAIN);
	BIND_ENUM_CONSTANT(GEN_EDIT_STATE_MAIN_INHERITED);
}
PackedScene::PackedScene() {
	state = Ref<SceneState>(memnew(SceneState));
}