### 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)

int parent_node = NO_PARENT_SAVED;
	if (save_node) {
		
		node_map[p_node] = idx;
		
		if (p_parent_idx == NO_PARENT_SAVED) {
			int sidx;
			if (nodepath_map.has(p_node->get_parent())) {
				sidx = nodepath_map[p_node->get_parent()];
			} else {
				sidx = nodepath_map.size();
				nodepath_map[p_node->get_parent()] = sidx;
			}
			nd.parent = FLAG_ID_IS_PATH | sidx;
		} else {
			nd.parent = p_parent_idx;
		}
		parent_node = idx;
		nodes.push_back(nd);
	}
	for (int i = 0; i < p_node->get_child_count(); i++) {
		Node *c = p_node->get_child(i);
		Error err = _parse_node(p_owner, c, parent_node, name_map, variant_map, node_map, nodepath_map);
		if (err) {
			return err;
		}
	}
	return OK;
}
Error SceneState::_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) {