### 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)

ERR_FAIL_INDEX(p_signal, names.size());
	ERR_FAIL_INDEX(p_method, names.size());
	for (int i = 0; i < p_binds.size(); i++) {
		ERR_FAIL_INDEX(p_binds[i], variants.size());
	}
	ConnectionData c;
	c.from = p_from;
	c.to = p_to;
	c.signal = p_signal;
	c.method = p_method;
	c.flags = p_flags;
	c.unbinds = p_unbinds;
	c.binds = p_binds;
	connections.push_back(c);
}
void SceneState::add_editable_instance(const NodePath &p_path) {
	editable_instances.push_back(p_path);
}
String SceneState::get_meta_pointer_property(const String &p_property) {
	return PackedScene::META_POINTER_PROPERTY_BASE + p_property;
}
Vector<String> SceneState::_get_node_groups(int p_idx) const {
	Vector<StringName> groups = get_node_groups(p_idx);
	Vector<String> ret;
	for (int i = 0; i < groups.size(); i++) {
		ret.push_back(groups[i]);
	}
	return ret;
}
void SceneState::_bind_methods() {