I noticed my zoom-in behavior occurred more like every 60 seconds, not a few times per minute. Then I thought about keyboard shortcuts. Then it dawned on me: I use Caffeine, a utility that keeps windows from going to Sleep. Caffeine simulates an F15-up-key action. I disabled it, and the unwanted zoom-in behavior has seemingly stopped. Apparently, there is some interaction with an F15 key and Affinity Designer.
So if you're using a keep-awake utility, then it could be the culprit for the unwanted zoom-in.
Those purple lines are there to indicate the snapping candidates. You can disable them by clicking on the little white triangle next to the Snapping magnet and clearing the 'Show snapping candidates' checkbox in the dropdown panel.