As with all winter breaks, but especially in a longer break, division and department leaders are responsible for ensuring that external contacts are aware of the closures and as appropriate salaried staff are performing services as necessary to meet the needs of the community during the closure, including checking email/voicemail and responding to time-sensitive matters.
The OOO definitely has those two pieces. But it could be 1 of 4 people who handle things when I’m out (depending on what it is) and they may not know at all that the requestor had reached out to me first / forget to cc me. So, I’d see this as me adding to my OOO “if you contact person X, please keep me cc’ed on the message you send to person x”?

There ought to be a word - and perhaps there is, in German - for the mix of feelings that accompanies composing and activating a holiday out-of-office message. There's smugness, of course, and a gratifying sense of laying down one's virtual tools after a horribly long shift. But for many of us, these nice feelings are tempered by the knowledge that in two weeks, refreshed but depressed, we will have to trawl through hundreds of emails, many of which will be conference room notifications for meetings about crises that have passed.
Regardless of my general health and hygiene over the silly season, I’ll be back in the office on January 2. 15. “Thank you for your consideration during this festive or not-festive time.”