Incoming emails going to trash (no rules set)
As mentioned in a comment by @negacao another way to view mailbox rules is to use the webapp:
Webapp -> Gear Icon -> Options -> Organize Mail -> Inbox Rules
There was, in fact, a rule set there which I had completely forgotten about. Disabling the rule allows messages to come to the inbox from the SMTP server, which indicates this was the root of the problem.
This same rule is not visible anywhere within Mail.app, for some reason.
The moral of the story for me is, "when in doubt, check the webapp".