What exactly happens when I delete a to-do?

Deleting a to-do removes it from this app AND from your Supernote (it propagates to the cloud and your device). If you'd already pushed that to-do to a connected app (Todoist, Reminders, or Google Tasks), the copy there is left untouched — it stays in your task app. So "Delete" clears it from Supernote's world but does not reach into your other to-do apps. The confirmation dialog tells you this (e.g. "will be removed from this app and your device. It stays in Todoist").