I know that the usual login to an anonymous account will not work at the moment. However I discovered if you search for an app in your browser and if you set up AuroraStore to open Playstore links, you can can still update your apps.
- Search for app in browser
- AuroraStore opens but "failed to fetch app details"
- Press back button
- You will find you are logged in to AuroraStore and can update your apps.