Hi Michel,
Apologies for the delay.
From the latest logs, it appears that the backup itself is completing successfully, and is now attempting to send the email (and not receiving an error back from the server).
If possible, please could you (or your server admin/hosts) check the logs for the outgoing mail server?
It is possible that the emails are being blocked at a lower level.
Are you receiving any other emails from the site?
Best Wishes,
Dee