I know how to add handlers to UnityEvents in code like below. However, I’d also like to update the Editor UI. Is this possible?

I figured it out. You have to add it via the UnityEditor instead:
UnityEditor.Events.UnityEventTools.AddPersistentListener(EnterEvent, townSceneEnterer.EnterLocation);
You also have to handle depuping if you need it. That is, don’t add the same event over and over.