My colleagues have this weird habit of not using out of office messages, but instead, sending all staff or all manager emails before they go on vacation letting everyone know they’re going to be gone for x amount of time. It’s really odd. I do not do this.
I go with “offline” or “away” (away…to my couch). I like closing the door, though!

I think it’s irritating and condescending and could have been funny if only one of the goofy elements was incorporated, instead of trying to make a cohesive comedy bit. It seems like the points should be reversed. Most urgent to least urgent. If I have a truly urgent issue I don’t want to read through that I should ask myself if it’s important and urgent. If it’s something that can wait, I’ll just expect a delay. If it’s not important or at least worth communicating, I wouldn’t be sending the email.
I’ve had several co-workers over the years use “at my earliest convenience” and it’s always rubbed me the wrong way. It just sounds kind of dismissive like, “I don’t care when you need it, I’ll get to it when I get to it.”