After the errata, is the Zhonya's Hourglass trigger optional or automatic?

Ruling: Zhonya's Hourglass trigger is automatic, not optional. The errata did not change this aspect of the card.

Nuances:

• There is nuance around when you might or might not have to play a hidden Zhonya's under the new rulebook
• In the new 1.1 rules, if you control a battlefield during combat (even if all your units die), you don't lose control until combat is over, so you can wait until later in the showdown to play Zhonya's from hidden
• In the old rules, once your last unit died you would lose the hidden Zhonya's immediately if you didn't play it
• When a unit is killed by an effect like Hextech Ray during a showdown, you must react with Zhonya's before that effect resolves if you want to save that specific unit