### 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)

} while (ss.is_valid());
	return false;
}
Vector<NodePath> SceneState::get_editable_instances() const {
	return editable_instances;
}
int SceneState::add_name(const StringName &p_name) {
	names.push_back(p_name);
	return names.size() - 1;
}
int SceneState::add_value(const Variant &p_value) {
	variants.push_back(p_value);
	return variants.size() - 1;
}
int SceneState::add_node_path(const NodePath &p_path) {
	node_paths.push_back(p_path);
	return (node_paths.size() - 1) | FLAG_ID_IS_PATH;
}
int SceneState::add_node(int p_parent, int p_owner, int p_type, int p_name, int p_instance, int p_index) {
	NodeData nd;
	nd.parent = p_parent;
	nd.owner = p_owner;
	nd.type = p_type;
	nd.name = p_name;
	nd.instance = p_instance;
	nd.index = p_index;
	nodes.push_back(nd);
	return nodes.size() - 1;
}
void SceneState::add_node_property(int p_node, int p_name, int p_value, bool p_deferred_node_path) {