How to automatic backups work with block storage volumes? Are they included in backups of the Droplet they're attached to, or do they get backed up on their own? And if they get backed up, how does the pricing work?
Backups of Block Storage is not available for now.
Block Storage volumes are High Available and Redundant - it reduces chance of data loss in case of hardware failure.
This is quote from Announcement - Block Storage: More Space to Scale:
Block Storage stores data on hardware that is separated from the Droplet
and replicated multiple times across different racks,
reducing the chances of data loss in the event of hardware failure.
If you want to take backup of it, you can do it manually via Snapshots. Snapshots are priced $0.05/GB/month.
If you want to leave feedback on this or suggest is as idea, you can head over to DigitalOcean UserVoice page.