I'm running a Proxmox cluster and the backup jobs were using the legacy e-mail system, which apparently sends e-mail directly from the Proxmox host (???), which my mail hoster declined due to them being unencrypted in transit.
However the Proxmox admin account would receive an "Undelivered Mail Returned to Sender" notice with the content of the original mail and _that_ would be sent through the notification system which is properly set up.
Task failed successfully? 🥴

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