If you are checking emails while you’re out and are responding slower than normal, state that, suggests Jill Gugino Panté, director of the Lerner Career Services Center at the University of Delaware. “If you don’t have access to email and can’t return messages, state that as well,” she says. “The clearer you are in your messaging, the better.”
Education Details: 15 Out of Office Messages for Professionals. February 26, 2021. Out of office messages are automatic email replies, or autoresponder email messages, that go out to colleagues, customers and clients when you are away from work. They let others know you are unavailable for contact and when they can expect a response to their emails.

I worked at a public agency and would have different out-of-office messages for internal and external. I was chastised for having a “too informal” message- because the idiot talking to me didn’t realize me saying “I’ll be back next Tuesday for the big staff meeting” (or whatever) was just for co-workers and not the public. I told them but of course it didn’t matter. So from then on I always made sure to start my internal OOOs- “Hello Company X comrade…. blah.” So it was clear which was which. I am not able to respond to your email promptly because my husband died. I will not be accepting zoom invitations. Please do not respond by suggesting future alternative dates. I don’t know when I will be able to speak without crying.
(first line in the second one refers to the new exec for our function starting that same week – an internal move). If I can get the date I’ll be back into the haiku I do, otherwise I put it afterwards, along with the person to contact in my absence. Obviously if I’m off sick or otherwise can’t be bothered I don’t do the haiku.