I've just discovered that /var/lib/cobbler has a .git respository, but it stopped getting commits about a month ago. All the commit messages are "API update" - presumably from the web interface.
I find that "cobbler sync" on the command line generates a commit message of "API update". Changes via the web interface are not committed to the repository unless one clicks the "Sync" action in the left side panel.
For myself, the odds of forgetting to hit that "Sync" link on at least some occasion are vanishingly close to 100%, even now that I understand I'm supposed to use it. I'm going to add a nightly - perhaps even hourly - "cobbler sync" invocation in cron.