Once the person reaching out to you realizes you’re gone, they may panic if they have a legitimate need for immediate support. The best way to avoid this is to let your callers (and emailers) know how to find the appropriate help.
Okay. So, it’s not to my exact personal tastes — to me, it’s overly wordy — but it’s probably fine for their culture and I’d be mildly amused if I got it. I see where you’re seeing condescension, but I think you can read it without that too.

Oh my gaaaaawwwwdddd my mother used to do this. Like, her work voicemail was “Hello, you have reached Lizy’s Mother, Job Title at Company Name. Today is Thursday, June 3. I am in the office today, but away from my desk at the moment. If you’ll leave a message with your name, phone number, and reason for your call, I’ll get back to you as soon as I can.”
If I’m out for three months, *someone* is doing each bit of my job in that time. Me coming back and wading through three months of emails where the majority of them will involve someone seeing the OOO and promptly emailing my cover instead, and trying to track down which ones did that and cc-ed me, which ones did that and *didn’t* cc me, and which ones fell off is just a terrible use of getting-back-up-to-speed time.