"I've been running Debian on servers for well over a decade now and have never had an update break something. Never. "
Then you haven't been using it long enough. Back when Woody became Sarge (2005) the dist-upgrade broke something truly central: cron. To be precise the upgrade caused the /etc/crontab file to be overwritten with a default version, no questions asked.
Sure there are other crontabs and they survived just fine but at the time the mantra was to put everything into that one file, which we did. It was a hosting environment so more or less everything was to be executed by root, and this included backups. The crontab also held the backup verification so neither the backup ran nor the job that should alert if it failed somehow. Some months later one upgraded server died due to bad disks and 30 mins later another. They were built with disks from the same batch and they failed like clockwork. On the backup system the retirement of old backups worked like a charm however, leaving no backups of the affected servers... Not really fun.
1) Don't ever dist-upgrade a production server. Build a new server with the new distro and transfer the data.
2) Have the backups checked by an independent system.
3) Retire old backups by number left, not age.