I think that’s maybe something you need to deal with internally with the person/people who you’re asking people to speak to instead – I think if you start to ask the original sender to update you or cc you then it’s going to start to annoy people that they are doing the running around, plus not everyone will do it.
But your out-of-office message is as much for you as it is for the people receiving it, especially during the pandemic. “Boundaries have taken a big hit right now,” Ritter says. There’s a lot of pressure associated with missing something at work, and that stress has been heightened without the typical separation between office and home and with the added fear caused by an uncertain economy. An OOO message is a chance to set expectations, “to give yourself some breathing room and to ensure other people aren’t thinking negatively about you,” Ritter says, and it’s crucial for your mental health.

I guess I generally dislike ones where the person is actually around but just might take longer than usual to answer emails (except in public-facing inboxes, etc.) I understand that if I’m using email, you might not respond right away.
After X enjoyable years, I do not work at [company] any more. Please contact [insert name and email] for enquiries relating to [subjects], or myself at [email] for personal matters.