### 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)

if (p_drag_data["type"] != "nodes") {
		return false;
	}
	Array nodes = p_drag_data["nodes"];
	if (nodes.size() != 1) {
		return false;
	}
	Node *dropped_node = get_tree()->get_edited_scene_root()->get_node(nodes[0]);
	ERR_FAIL_NULL_V(dropped_node, false);
	if (valid_types.is_empty()) {
		
		return true;
	}
	for (const StringName &E : valid_types) {
		if (dropped_node->is_class(E) ||
				EditorNode::get_singleton()->is_object_of_custom_type(dropped_node, E)) {
			return true;
		}
	}
	return false;
}
void EditorPropertyNodePath::update_property() {