### 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)

np = p_dictionary["node_paths"];
	}
	node_paths.resize(np.size());
	for (int i = 0; i < np.size(); i++) {
		node_paths.write[i] = np[i];
	}
	Array ei;
	if (p_dictionary.has("editable_instances")) {
		ei = p_dictionary["editable_instances"];
	}
	if (p_dictionary.has("base_scene")) {
		base_scene_idx = p_dictionary["base_scene"];
	}
	editable_instances.resize(ei.size());
	for (int i = 0; i < editable_instances.size(); i++) {
		editable_instances.write[i] = ei[i];
	}
	
}
Dictionary SceneState::get_bundled_scene() const {
	Vector<String> rnames;
	rnames.resize(names.size());
	if (names.size()) {
		String *r = rnames.ptrw();
		for (int i = 0; i < names.size(); i++) {
			r[i] = names[i];
		}
	}
	Dictionary d;
	d["names"] = rnames;