Given that @Zimmy doesn’t see the plug orientation problem on his L5USA, and @guru, @steve and @amarok don’t see the problem on their L5, I think that we can conclude that this is a defect in my device. I added this note to the article:
EDIT: Other L5 owners have commented on the Purism forum that they can charge using both sides of the USB-C plug, so this plug orientation problem is probably caused by a defect in my device, which I have sent back to Purism for servicing.