Okay, since the email server is separate, forget what I said. In your original message you said "I have my email server on the same server as my Plone site" but it sounds like you meant a separate server from the same provider.
The Plone docker images do not include an SMTP server. You are expected to configure Plone to use an external SMTP server, not localhost. In this case it sounds like you need to use smtpout.secureserver.net or host.secureserver.net (I'm not sure which, you mentioned both above).
In Docker, logs for the container's main process typically go to stdout rather than to a file. The Docker host captures them and you can view them with docker logs [container id]. For the Plone backend image, these are the logs you are used to finding in the instance log. There is no separate SMTP log, because there is no SMTP software included.