Looks like my credit card needs to be updated at Amazon AWS, and my backups stopped working. I got notifications about the failed backups, but no reason why. Visiting the backups page, I saw a 404 error. This topic might be FAQ material for those who follow, or a feature request to improve the error reporting. Seems to me the reason for the error could be visible on the backups page, or even in the notification.
Visiting the logs, I get a decent clue:
Failed to list backups from S3: The AWS Access Key Id you provided does not exist in our records.
You now get a popup with the error message from the S3 API instead of the generic error page when something went wrong while Discourse tried to access the backup bucket.