Published commentaries, with insights
The stories of Jonah and Jesus in boats are quite similar, so the question becomes one of whether the story of Jonah in some way prefigures that of Jesus or whether the story of Jesus calming the storm was substantially based on the story of Jonah.
Many commentaries that find prefigurement in the Book of Jonah really only focus on the three days Jonah spent in the belly of a whale as a prefigurement of the Resurrection, suggesting that these authors do not find the parallels with Jonah 1:4-5 to be very compelling. One such example is An Introduction to Jesus and the Gospels (pages 156, 354) by Frederick James Murphy.
Hahn, Mitch and Walters (Gospel of Matthew: Ignatius Study Bible, page 38) describe Jesus as the new Jonah, not only because he calmed a storm but even more so because his three days in a whale prefigured Jesus' three days in the tomb.
Alonzo L. Gaskill (Miracles of the New Testament: A Guide to the Symbolic Messages) lists the parallels between the two miracles and finds them strong and obvious, but reaches no conclusion.
The first New Testament gospel to be written was Mark's Gospel, so Timothy Keller (King's Cross: The Story of the World in the Life of Jesus) looks to Mark for an explanation. He says that Mark has deliberately laid out his account using language that is parallel, almost identical, to that in Jonah. Although Jesus is not tossed into the sea, as was Jonah, he says that Mark is showing that the stories are not actually different when you stand back a bit.
Robert M. Price says in The Christ Myth Theory and Its Problems, page 80, that Jonah 1:4-6 forms the basis for Mark 4:35-41, with elaboration via Psalm 107:23-29. He cites Dennis R. MacDonald in The Homeric Epics and the Gospel of Mark, pages 68, 174-175, as identifying a parallel between Mark 4:35-41 and Odyssey 10:1-69, with particular reference to Jesus' rebuke of the disciples (4:40) and the puzzling "there were also with him other little ships" (4:36). In copying from Mark, the author of Matthew omitted the reference to the other boats accompanying them.