Honestly, what drives me crazy is after someone has emailed me, gets the out of office, then *does* email someone else instead of waiting for me to get back. Yet said someone doesn’t email me back to say “see you’re out, person X got it taken care of, you can disregard my email”. So then I waste time seeing the initial request and following up. Has anyone found a good wording / other solution to know if the request was completed by someone else?
If their message is urgent or they’d like to contact someone else instead, you can let them know what to do.

Funny emails are getting trendy, but they have to be used properly. If you are absolutely sure that your recipients will have a chuckle, go ahead and write a funny out-of-office auto-reply. It might make their day.
Yeah, announcing you were going to delete emails unread and expecting the sender to resend when you return would NEVER fly in my office. I’d get executive complaints about that, especially if it went to a client or outside party – if a client can’t reach you, they will reach out to someone else who may not work at your organization and you lose business. I feel like this delete-it-all philosophy would only work for an entirely internal role where timelines are more relaxed, and even then, I feel it’s a bit unprofessional to foist your own catch-up work onto others, especially if they’ve been backfilling for you while you were OOO.