### 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)

Vector<Property> properties;
		Vector<int> groups;
	};
	struct DeferredNodePathProperties {
		Node *base = nullptr;
		StringName property;
		NodePath path;
	};
	Vector<NodeData> nodes;
	struct ConnectionData {
		int from = 0;
		int to = 0;
		int signal = 0;
		int method = 0;
		int flags = 0;
		int unbinds = 0;
		Vector<int> binds;
	};
	Vector<ConnectionData> connections;
	Error _parse_node(Node *p_owner, Node *p_node, int p_parent_idx, HashMap<StringName, int> &name_map, HashMap<Variant, int, VariantHasher, VariantComparator> &variant_map, HashMap<Node *, int> &node_map, HashMap<Node *, int> &nodepath_map);
	Error _parse_connections(Node *p_owner, Node *p_node, HashMap<StringName, int> &name_map, HashMap<Variant, int, VariantHasher, VariantComparator> &variant_map, HashMap<Node *, int> &node_map, HashMap<Node *, int> &nodepath_map);
	String path;
	uint64_t last_modified_time = 0;
	static bool disable_placeholders;
	Vector<String> _get_node_groups(int p_idx) const;
	int _find_base_scene_node_remap_key(int p_idx) const;
protected:
	static void _bind_methods();
public:
	enum {