### 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)

edit->set_disabled(p_read_only);
}
void EditorPropertyObjectID::_edit_pressed() {
	emit_signal(SNAME("object_id_selected"), get_edited_property(), get_edited_property_value());
}
void EditorPropertyObjectID::update_property() {
	String type = base_type;
	if (type.is_empty()) {
		type = "Object";
	}
	ObjectID id = get_edited_property_value();
	if (id.is_valid()) {
		edit->set_text(type + " ID: " + uitos(id));
		edit->set_tooltip_text(type + " ID: " + uitos(id));
		edit->set_disabled(false);
		edit->set_icon(EditorNode::get_singleton()->get_class_icon(type));
	} else {
		edit->set_text(TTR("<empty>"));
		edit->set_tooltip_text("");
		edit->set_disabled(true);
		edit->set_icon(Ref<Texture2D>());
	}
}
void EditorPropertyObjectID::setup(const String &p_base_type) {
	base_type = p_base_type;
}
void EditorPropertyObjectID::_bind_methods() {