If a system's timezone is updated, rsyslog doesn't find out about
it. Arguably, this only applies to travelling laptops, but rsyslog
is the default Debian logger on this, which is why I think this is
worthwhile to think about.

Many other tools automatically adjust on timezone changes, whether
that is through inotify on /etc/localtime, not caching the timezone
in the first place, or some other mechanism provided by the OS.

Please consider something similar for rsyslog.