The error mail is sent by the CRON daemon, running on your host's operating system, not Joomla!'s mail class. Receiving that email doesn't mean that the Joomla! mail class works. It means that your host's server can send out emails. AS I told you, the problem is with Joomla!'s email setup, not your host's email setup.
The backups taken from the administrator panel
do not send out any emails. Line 108 of administrator/components/com_akeeba/akeeba/core/domain/finalization.php checks the backup origin. If it's originating from the back-end no email is ever sent by Akeeba Backup. If you take a look at the log file produced by a back-end backup you'll see no sign of the "Preparing to send e-mail to administrators" message which indicates the initialization of the mailer procedure. So, what you say it happens can't be happening by any means (you getting an email from a
back-end backup job on success and failure).
At this point I still do not know with any degree of certainty that your Joomla! site is properly configured to send out emails. Please do check your site's email configuration as proposed in my previous reply:
make sure that you can send emails from your site, i.e. that an email is sent if you use the Mass Mail feature or when a new user registers on your site.
Does this work? I really need this information to help you, otherwise I wouldn't have asked for it :)
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!