### 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)

if (base_scene_idx >= 0) {
		Ref<PackedScene> ps = variants[base_scene_idx];
		if (ps.is_valid()) {
			return ps->get_state();
		}
	}
	return Ref<SceneState>();
}
void SceneState::update_instance_resource(String p_path, Ref<PackedScene> p_packed_scene) {
	ERR_FAIL_COND(p_packed_scene.is_null());
	for (const NodeData &nd : nodes) {
		if (nd.instance >= 0) {
			if (!(nd.instance & FLAG_INSTANCE_IS_PLACEHOLDER)) {
				int instance_id = nd.instance & FLAG_MASK;
				Ref<PackedScene> original_packed_scene = variants[instance_id];
				if (original_packed_scene.is_valid()) {
					if (original_packed_scene->get_path() == p_path) {
						variants.remove_at(instance_id);
						variants.insert(instance_id, p_packed_scene);
					}
				}
			}
		}
	}
}
int SceneState::find_node_by_path(const NodePath &p_node) const {