You should upgrade your barman server. This is a known issue related to concurrent backups (the only kind of supported backup since Postgres 15) where the connection to the server is killed by some external source (keepalive on a router, maybe), and then Barman can't stop the backup.
We introduced an enhancement in 3.11 that keeps the connection alive so that other appliances in the network don't see it as a dangling idle connection and kill it.
I would particularly recommend upgrading to the latest 3.17, which has a lot more things that we've fixed. Please check the release notes.