One of the key things for me about zeners is to realize that in a reverse bias situation (current flowing from cathode to anode), the current is still flowing when the zener voltage is reached. I always visualize diodes as a “brick wall” when in a reverse bias situation, but it’s really that the voltage to get up over that wall is normally high enough that it’s not practical. A zener is specifically made to lower the voltage of that “wall”. Not sure if that visualization helps others, but it was helpful for me.
I did not mention it in my original post, but the aspect I liked about this article was again this focus on looking at understanding how the current flows and not just the voltage.