App Volumes stores all configuration information in the App Volumes database, and the App Volumes Manager servers operate independently of one another. Owing to this, there is no critical information to back up on the App Volumes Managers servers themselves, although if custom SSL certificates were installed you may wish to retain backups of those.
If your environment uses Writable Volumes, it is important to be able to recover the underlying storage configuration and contents. App Volumes manages writable volume assignments based on where the volume was first created, and, if those Writable Volumes are restored to an alternate location, their connection to the clients would be lost until they are imported and manually assigned.