I take advantage of the ability to send different OOO messages to internal or external addresses. Internal addresses get a couple of people to contact if it’s urgent, usually my direct report and my backup person, since between them they can cover pretty much everything I do, or at least they’ll know who can. External addresses get a more general notice: “I am temporarily out of the office. If your message is regarding the Llama Care project and requires a prompt response from our Llama Grooming Team, please make sure that [email protected] is one of the recipients of your message.” Probably not the most elegant phrasing, but we have a distribution list for this very reason. Even requests that they know only I handle are supposed to go to the LG list.
About the “overshares”: You linked to a previous column that mentioned this point, “Sometimes the over-sharing of plans can even come across as suspect — similar to how when someone’s calling in sick with genuine illness, they usually just say, ‘I’m going to be out sick,’ but fakers will generally give you a long list of overly specific symptoms, like they feel they have to convince you.”

we had something similar at one phone-heavy place I used to work and it was actually extremely useful – everyone set their voicemail when they got in, and people would include if they were offsite (so worth ringing their mobile) or likely to be otherwise unreachable, and who to contact if your query was urgent. only took a minute to set, and was super useful to me as someone who had to talk to maybe 10-20 people on the phone in a day.
Your business is important to us and I will respond to you immediately when I return to work.