Phone gets stuck on the clock
It turns out it's the "smart cover" feature (the thing that displays time when you close a flip-case-with-a-window), which was misfiring probably because of the presence of a nearby magnet (likely the one in my holster's cover) or some problem in my phone's magnetic sensor.

This feature can be disabled in Settings =&gt; Connected Devices =&gt; Smart Cover.

See the reddit thread where I found my answer.