The kraken enters print as natural history rather than as folklore. Erik Pontoppidan, Bishop of Bergen, described it in his natural history of Norway published in the early 1750s, reporting the accounts of fishermen: a creature so broad that sailors mistook its back for an island, whose descent pulled a whirlpool, and whose feeding grounds fishermen sought out because the fishing above it was good. Pontoppidan was collecting testimony and presenting it as fact, which is what a naturalist of that period did.
The nineteenth century supplied an animal. Large squid carcasses came ashore in Newfoundland and elsewhere in the 1870s, specimens reached museums, and the genus Architeuthis was described. A giant squid does not sink ships and is not the size of an island, but it is large, it has arms, and it was unknown, which was enough for the identification to stick.
That identification is a modern reading and should be labelled as one. It explains some of the reports and it does not explain the island, the whirlpool or the fishing ground. What the sequence does show is a monster moving in the opposite direction from the usual one: not a real animal exaggerated into a legend, but a legend that a real animal was later recruited to explain.