You can literally see the lightning come off Big Mom when the missiles are destroyed which has always represented Kings Haki post timeskip.Why does everyone keep saying big moms conquers Haki is doing all this amazing stuff. Her screaming is what is holding all those pirates back as soon as katakuri gave everybody ear plugs everybody can move. Her scream is what destroyed the missiles and the mirror not her Haki stop saying that your giving feats to the wrong things.
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You can even see people start foaming at the mouth when she initially activates it
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Its clearly a combination of a scream and kings haki, but the scream is only painful on their ears, it isnt the thing thats creating the gust and electricity