How did "black wok" semantically shift to mean definition 2 above? In 2020, Chinese cooking require woks that are usually black, so I can't imagine how it appertains to 'blame for a crime'?
The Cantonese equivalent of 背黑鍋 is 替人孭鑊
鑊 is a slang for 'incident' e.g. 大鑊 (big wok = big incident). 孭鑊 (to carry the work) means 'to take the responsibility/ blame (for an incident or mistake)' . "替人孭鑊" = "take blame for someone else" = "背黑鍋" in Mandarin