Coworkers, clients, and subscribers typically expect fast responses and solutions to their problems, particularly from people working in customer service, marketing, and communications jobs. Out of office messages provide them with a polite, concise, and professional explanation of why you cannot respond right away. You can provide an OOO message if you are gone for one day, one week, or several months.
I personally always leave my employee as my contact because a) I trust her completely, b) I’d prefer people email her anyway, so this is nice practice, c) My boss is the CEO so please for the love of god don’t email him about your data entry issue, d) the people who are emailing me about sensitive things that my employee shouldn’t know about also know enough to have that discretion.

Setting your out of office may be different depending on the email provider you use. But whether you’re on Outlook, Gmail, or another platform, it should be a relatively straightforward process.
I don’t. They just have to wait. The people in my office that could have a legitimate emergency that requires my input have my cell number, and they’d just call me.