We had someone at my old job whose auto-reply stated that they were at a “White Privilege Conference”. Granted, the conference was about dismantling White Privilege, but to someone outside our work who didn’t know that, I imagine that got quite the reaction!
I usually go with “Hickory, dickory, dock, I’m off the clock. When the clock strikes Tuesday, I’ll be back.”

I thought it was funny but could never get away with using something like that at my org. I loved the “competent people who work for me” part – I make this joke all the time. We have some people who feel that they should have a manager personally attend to them and, at least in my case, my highly competent team is in the weeds of that work a lot more and are not rusty (like I am).
I struggle with naming a contact too. My current job doesn’t really have emergencies, so while my second in command could handle stuff I normally would, should she have to? Also, 98% of the people that would get my OOO would know who to go to anyway if they actually needed something urgent. I hate to make someone else’s life harder for my own convenience when it’s not even needed.