Last time I checked, Barman didn't support backups to S3. That's why (for us) pgBackRest was such a big deal: it could offload full and incremental backups to a basically limitless and reliable medium.
I think (and I'm probably wrong now) that Barman only could push backups to another Linux machine (e.g., EC2 box), so you had to worry about your backup system _on top_ of the main DB.
So I'm really hoping someone will pickup maintaining pgBackRest.