`DateTime` arithmetic on `Microsecond` (or smaller) scale

Let’s continue the discussion on UT vs UTC over in Universal Time vs UTC Time in Dates and try to keep this topic on the higher precision arithmetic. My split wasn’t perfect here, but I tried to preserve as much as I could. In doing so, I unfortunately ran into some Discourse bugs, which placed some posts completely out of order. Please ping me if you see anything that’s still out-of-place or nonsensical in its (possibly new) context, but I think I got it now.