I’ve always used “excuse me?”, “pardon?” or something like “I’m sorry, I didn’t get that” or some such.
To me, though I’m American, “what?” sounds almost rudely abrupt and in many cases is used as an “I can’t BELIEVE you just said that!” or “You’re KIDDING” type expression.
“Huh?” just sounds moronic and lazy. And I am moronic and lazy enough to use “huh?” occasionally, when it comes to just friends and family (then I always mentally kick myself and think UGH that sounded so lovely, NOT!), but never in business or social interactions.
At least in Commonwealth English ‘pardon’ is typically a contraction of “I beg your pardon” so maybe its a residual memory of class distinctions in play. The upper classes don’t need to beg anyone’s pardon so they just said ‘what?’, the lower classes while dealing with their social superiors might have learnt a bit of grovelling. “Begging your pardon guv”