### Godot version

4.1.dev4

### System information

Windows 10 Godot 4.1.dev4

### Issue description

The watched property in the Multiplayer Synchronizer node is supposed to pass the variable through the network only when it changes, but as I use the network profiler, it is evidently not working as intended

### Steps to reproduce

Open 2 debug instances on the project I will give, use the network profiler and you will see the variable does not change, although it goes up to 780b/s on the network

### Minimal reproduction project

[minimalproject.zip](https://github.com/godotengine/godot/files/11659414/minimalproject.zip)

if (deleting.is_empty() || config.is_null()) {
		return;
	}
	if (p_confirmed) {
		const NodePath prop = deleting;
		int idx = config->property_get_index(prop);
		bool spawn = config->property_get_spawn(prop);
		bool sync = config->property_get_sync(prop);
		bool watch = config->property_get_watch(prop);
		EditorUndoRedoManager *undo_redo = EditorUndoRedoManager::get_singleton();
		undo_redo->create_action(TTR("Remove Property"));
		undo_redo->add_do_method(config.ptr(), "remove_property", prop);
		undo_redo->add_undo_method(config.ptr(), "add_property", prop, idx);
		undo_redo->add_undo_method(config.ptr(), "property_set_spawn", prop, spawn);
		undo_redo->add_undo_method(config.ptr(), "property_set_sync", prop, sync);
		undo_redo->add_undo_method(config.ptr(), "property_set_watch", prop, watch);
		undo_redo->add_do_method(this, "_update_config");
		undo_redo->add_undo_method(this, "_update_config");
		undo_redo->commit_action();
	}
	deleting = NodePath();
}
void ReplicationEditor::_update_checked(const NodePath &p_prop, int p_column, bool p_checked) {