Someone told me not to ask strangers how their day was (like in the real world) if I didn’t really want to know (like that someone’s dad died)

To be fair, this is cultural. I’m an American immigrant in Germany, and I’ve unintentionally started that type of conversation a bunch of times. Here, if you ask, it’s not a social cliche, so you shouldn’t be unprepared for a real answer. In American terms, it’d be like putting your hand on someone’s shoulder, looking them in the eye for a moment and asking “how are you?,” then being surprised if they tell you something sad.