Nothing has released the Android 13 update:

https://9to5google.com/2023/02/16/nothing-phone-android-13-update/

Over on XDA Developers there are links directly for updating for both beta testers as well as those on 1.1.8:

https://forum.xda-developers.com/t/nothing-phone-1-rom-ota-nothing-os-repo-of-nothing-os-update-16-02-2023.4464039/

I've updated mine, everything is working, slightly improved performance and responsiveness. Working well so far.