IME people rarely test and drill for the failovers, it's just a checkbox in a high level plan. Maybe they have a todo item for it somewhere but it never seems very important as AZ failures are usually quite rare. After ignoring the issue for a while it starts to seem risky to test for it, you might get an outage due to bugs it's likely to uncover.
Replying to myself - also in this case people are reporting that load balancing service provided by AWS failed so it doesn't necessarily help if your own stuff is tested and working.