### 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->can_instantiate();
}
Node *PackedScene::instantiate(GenEditState p_edit_state) const {
#ifndef TOOLS_ENABLED
	ERR_FAIL_COND_V_MSG(p_edit_state != GEN_EDIT_STATE_DISABLED, nullptr, "Edit state is only for editors, does not work without tools compiled.");
#endif
	Node *s = state->instantiate((SceneState::GenEditState)p_edit_state);
	if (!s) {
		return nullptr;
	}
	if (p_edit_state != GEN_EDIT_STATE_DISABLED) {
		s->set_scene_instance_state(state);
	}
	if (!is_built_in()) {
		s->set_scene_file_path(get_path());
	}
	s->notification(Node::NOTIFICATION_SCENE_INSTANTIATED);
	return s;
}
void PackedScene::replace_state(Ref<SceneState> p_by) {