I don't know about bcachefs' capability on this but with zfs, you can do an instant snapshot of MySQL/PostgreSQL data directory and call it a backup instead of fighting the tough fight that is database backup with their dump utilities taking a good amount of space and time and not easy to do incremental backups.

https://lackofimagination.org/2022/04/our-experience-with-po...

https://www.percona.com/blog/2017/12/07/hands-look-zfs-with-...