There are two things: The first thing is the fact that your server is trying to send mail through an external SMTP server and fails. The second thing is whether the cause is an empty From mail address as you suspects.
We have a major problem is studying the logs because the HTML editor of the forum discards/reformats part of the logs. The most notorious one is it discards HTML tags like <bla bla>. Also the domain name of the SMTP host 'email-smtp-us-east-amazonaws' looks suspicous to me.
One approach is to test this SMTP accound independently of Moodle. For example you can configure your local Thunderbird to send mail through this server.
General help
Email "from" address
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