I usually put my boss in my OOO, because if something is so urgent that it needs to be delegated RIGHT NOW then it’s urgent enough that my boss should know about it, and he’s also in the best position to know who on the team to delegate it to based on everyone’s workloads and what can be dropped. But the most likely result is that whoever is emailing me either waits for me to get back because it’s not that urgent or goes to the next/backup person based on our central documentation about who to contact for particular issues.
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.

You may not think it, but an auto-attendant is an important part of your business. It is typically the first point of contact with your customers, as they will call your main number with sales inquiries, troubleshooting questions, etc.
Thank you for your correspondence. I am currently away from my computer and may be delayed in my response.