I’ll reply to your message promptly when I return. But, if you require immediate assistance, please send an email to [contact name] at [contact email] in my absence.
I just say “following my return to the office” because saying “as soon as possible” isn’t actually when I’m going to respond — I may have other priorities when I get back that take precedence over responding to a week old email that wasn’t important enough for them to contact my backup. That said, it doesn’t bother me when other people do it!

I think people still understand that out of office can refer to home office as well. But you could say “unavailable” or “away from work”.
This is what I’ve seen most often in my career. Problem is, the contact is almost always the admin. I’m the admin. Everyone’s idea of assistance is different. Often, I didn’t have the knowledge about the issue in order to be of any assistance. I wound up spending more time running around looking for answers than actually working on what was on my own plate. It’s exhausting. Otherwise known as “please don’t call us for unicorn problems when we handle llamas. Literally, we can’t do anything for unicorn problems.”