### 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)

rconns.push_back(cd.to);
		rconns.push_back(cd.signal);
		rconns.push_back(cd.method);
		rconns.push_back(cd.flags);
		rconns.push_back(cd.binds.size());
		for (int j = 0; j < cd.binds.size(); j++) {
			rconns.push_back(cd.binds[j]);
		}
		rconns.push_back(cd.unbinds);
	}
	d["conns"] = rconns;
	Array rnode_paths;
	rnode_paths.resize(node_paths.size());
	for (int i = 0; i < node_paths.size(); i++) {
		rnode_paths[i] = node_paths[i];
	}
	d["node_paths"] = rnode_paths;
	Array reditable_instances;
	reditable_instances.resize(editable_instances.size());
	for (int i = 0; i < editable_instances.size(); i++) {
		reditable_instances[i] = editable_instances[i];
	}
	d["editable_instances"] = reditable_instances;
	if (base_scene_idx >= 0) {
		d["base_scene"] = base_scene_idx;
	}
	d["version"] = PACKED_SCENE_VERSION;
	return d;
}
int SceneState::get_node_count() const {