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It basically tells you that the problem is within the host's infrastructure itself. Have you sent them this information?

Correct. If the backup finishes and it appears with a status of OK or Remote it is fine.

A slightly longer explanation. Whenever you see the yellow resume modal in the middle of taking a backup it's exactly because of servers like yours – actually, it's exactly because of the problems I had observed in the very host you are using. The servers are overcrowded and tend to rate limit, crash, or restart the web server service unexpectedly. This causes a disruption in the backup, typically with an HTTP 502 error. The problem clears within 10 to 30 seconds.

A long time ago, this kind of disruption would mean that your backup failed. It was annoying and frustrating. At one point I had the idea of resuming the backups after 10 seconds, and keep retrying that up to three times, giving enough time for these errors to clear. When this happens, the backup process rolls back to the last known good point (before the step that got interrupted started). This means truncating the backup archive, and rolling back the internal backup engine state to where it was before the interrupted step started. It will then retry that step.

This way, your backup never fails unless the server is at such a poor state that the backup has no chance of being recovered, or if it was a legitimate issue which can only lead to a failed backup.

The reason I asked you to check with your host is that if you get too frequent interruptions and your site is not on one of their cheapest plans if you complain about it they will move you to a less crowded server, significantly improving your experience. If you were given the corporate-polite version of "you can go pound sand" you're probably on a cheap enough plan that they effectively don't care to do that. At least you can rely on me doing everything in my power to work around your server to the fullest extent of what's humanly possible.