Maintaining that heading within 5 degrees or less is definitely a developed skill that most guys struggle with. Until the aircraft hits 40 KIAS it’s up to the pilot’s boots to keep it tracking straight out which is easier said than done.
I’ve not flown the 139, but other automated types I have will keep the heading very accurately if you keep your feet off the pedal micro switches, and typically do so even with some bank applied below a certain IAS, above which they revert to coordinated turn mode. It’s not even a function of the automation - it’s a fairly basic ATT mode AFCS function.