### 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)

}
			}
			resources_found.erase(r.ptr());
		} break;
		default: {
		}
	}
	return false;
}
void EditorPropertyResource::_resource_changed(const Ref<Resource> &p_resource) {
	Resource *r = Object::cast_to<Resource>(get_edited_object());
	if (r) {
		
		HashSet<Resource *> resources_found;
		resources_found.insert(r);
		bool found = _find_recursive_resources(p_resource, resources_found);
		if (found) {
			EditorNode::get_singleton()->show_warning(TTR("Recursion detected, unable to assign resource to property."));
			emit_changed(get_edited_property(), Ref<Resource>());
			update_property();
			return;
		}
	}
	
	
	bool is_script = false;
	Ref<Script> s = p_resource;
	if (get_edited_object() && s.is_valid() && get_edited_property() == CoreStringNames::get_singleton()->_script) {
		is_script = true;
		InspectorDock::get_singleton()->store_script_properties(get_edited_object());