Port logging to structlog.

Summary:
Our existing log infrastructure was not a scalable solution. We'll
funnel these structured logs into LogStash+Kibana or a similar toolchain
for searchable logs and visualizations.

structlog makes it easy to bind specific params to a given logger, so we
get more context for debugging. Awesome!

Also configure logging to just write to syslog instead of various files. This
requires a bit of configuration of rsyslog, but I think will ultimately make it
easier to set up remote log forwarding, log rotation and similar fancy stuff,
without having to worry about any of it in the actual application code.

Test Plan: Unit tests updated, and mailsync/api servers run.

Reviewers: spang

Reviewed By: spang

Differential Revision: https://review.inboxapp.com/D231