Why people greet others with the question:
To newcomers to Hong Kong, they may be surprised to learn that the standard greeting between local Chinese denizens is “Have you eaten yet?” or “nei sik jo fann mei a?” Taken literally, it might lead you to expect at a forthcoming lunch or dinner invitation. Not necessarily so.
The origins of this quaint phrase probably go back to darker days when food was not as plentiful as it is today. Eating was more of a cause for celebration, or at least relief. Therefore, the mere asking of the question evolved into a kind, courteous, and now routine greeting between friends; a show of care and concern.
I wonder if Chinese view the standard Western greeting of “How are you?” as equally quaint. After all, if it’s taken equally literally, it does invite a thorough update of your physical and mental health. I don’t think that is what is usually intended, so keep an open mind and enjoy learning about the culture of your new home.