### 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)

node = parent->_get_child_by_name(snames[n.name]);
#ifdef DEBUG_ENABLED
				if (!node) {
					WARN_PRINT(String("Node '" + String(ret_nodes[0]->get_path_to(parent)) + "/" + String(snames[n.name]) + "' was modified from inside an instance, but it has vanished.").ascii().get_data());
				}
#endif
			}
		} else {
			
			Object *obj = ClassDB::instantiate(snames[n.type]);
			node = Object::cast_to<Node>(obj);
			if (!node) {
				if (obj) {
					memdelete(obj);
					obj = nullptr;
				}
				if (ResourceLoader::is_creating_missing_resources_if_class_unavailable_enabled()) {
					missing_node = memnew(MissingNode);
					missing_node->set_original_class(snames[n.type]);
					missing_node->set_recording_properties(true);
					node = missing_node;
					obj = missing_node;
				} else {
					WARN_PRINT(vformat("Node %s of type %s cannot be created. A placeholder will be created instead.", snames[n.name], snames[n.type]).ascii().get_data());
					if (n.parent >= 0 && n.parent < nc && ret_nodes[n.parent]) {
						if (Object::cast_to<Control>(ret_nodes[n.parent])) {
							obj = memnew(Control);
						} else if (Object::cast_to<Node2D>(ret_nodes[n.parent])) {
							obj = memnew(Node2D);
#ifndef _3D_DISABLED