Did you forget “mail carrier” or “postal worker” were terms?
Postal workers maybe?
I’ve heard them called mail carriers. It’s more precise, for example my mum is a postal worker, but doesn’t carry mail (she has an office job with postal services).
Not exactly a story, but an ad from Australia post showing their evolution of delivery over the decades. https://youtu.be/T-ItHe5WxE4
I remember ads shown about how dogs run up to posites etc, so checked out their website.
Here are some other videos from them you might like.
Michael works at star track, a courier arm of Australia Post… https://youtu.be/V1AAj0qvyGc
And a postal worker. https://youtu.be/teLmg_2vF0w
I’m not associated with Auspost , but did watch the videos and OP, hope it helps. Posted on mobile so missed some details.
“This morning I looked in the personbox to see if the personperson had brought me any person”. --Spider Robinson iirc.