For anyone else that was confused, apparently there is an alternate usage of the word 'Cleave' that means 'to adhere' (rather than 'to cut' or 'to separate').[0]
I almost feel like that specific usage should come with the 'archaic' tag, but it's reasonably common in slightly older novels, I think? Things like "He still cleaves to the imagined ideals of his forefathers".
It definitely tends to be used in a more philosophical sense than the very physical "cleave a block of wood in two", though.
It definitely tends to be used in a more philosophical sense than the very physical "cleave a block of wood in two", though.