Never heard it mentioned that anyone is even aware of when a full moon will be
Ah ok, so you are not from Planet Earth. Greetings.
I've worked in healthcare for more than 20 years. I've never once heard of anyone psychologically preparing themselves for a full moon.
Well there you go, you learn something every day. The people you work with would probably never tell you anyway as they know exactly what kind of response they'd get. When I say "psychologically preparing" it's an internal knowing that there'll be more difficult customers in, that evening.
The energy at a full moon is higher, whether or not that's confirmation bias (but apparently it can't be as you claim that nobody knows about full moons anyway, so they aren't going to themselves "ok it's a full moon so I'll be deliberately driving around causing mayhem and kicking off this evening").
Retrospectively associating a busy night with a full moon is conformation bias
It's noticing a pattern that may or may not be related to the moon. I believe it is, you believe it isn't. Who cares. Either way, the moon waxes and wanes just like the sun rises and sets. So if you know that once a month things are getting a little hectic, you can also know that things will settle down again. Working with cycles - in any job not just healthcare - helps you to see that nothing is permanent, and that can help a lot with anxiety and stress.
There will have been countless worse nights that weren't on a full moon. What do we attribute those to?
Bad cup final result? I'd probably associate them with multiple patients with afflicted natal Neptunes arriving in A&E at the same time, but let's not go there.