I have been using barman indirectly through CloundNativePG with my latest company, but don't have the operational experience to speak on it yet.
When it’s set up properly, it’s solid as rock. I’d really recommend you check it out again; it likely solves everything you did more elegantly, and also covers a ton of things you didn’t think of. Been there, done that :)
For example, pgBackRest solves real problems with features like block level incremental backups that drastically reduce storage and transfer times for many workloads, automated backup retention policies, multiple repository support for offsite backup redundancy, encryption support, point in time recovery for granular restoration capabilities, and tooling to build standby servers very quickly and efficiently. These features handle edge cases and reduce operational overhead compared to managing scripts around pg_basebackup and WAL archiving yourself. In many environments, those features are required (e.g. encryption).
You are just wrapping pgdump, which is not a full featured backup solution. Great for a snapshot...
Use some of the existing tools and you get point-in-time recovery, easy restores to hot standbys for replication, a good failover story, backup rotations, etc.