When I create one of the various DrawActions via Draw. If the action completes, do I still need to clean up the event listeners I set up via the `.on()` method, or will those get cleaned up automatically upon completion?
Yeah, any listeners you create with "on" you need to clean up. The "on" method returns an object with a "remove()" method you can use for that.
https://developers.arcgis.com/javascript/latest/api-reference/esri-views-draw-DrawAction.html#on