It's pretty natural to read Jonah being swallowed by the fish (whale, if you like; I think the fights certain people have over whether it can be a whale are kind of hilarious misreadings of the doctrine of Scripture) as a typology, because Jesus himself pretty clearly says that it is:
But he answered them, “An evil and adulterous generation asks for a sign, but no sign will be given to it except the sign of the prophet Jonah. For just as Jonah was in the belly of the huge fish for three days and three nights, so the Son of Man will be in the heart of the earth for three days and three nights. Mt 12:39–40. NET
And yet I think we are mostly pretty down on the idea that Jonah 1 is a typology, because it seems to us that the sailors have incorrect theology and are in fact pagans, so their very idea that a god is angry and is going to sink the ship because they are carrying a sinful person seems... pagan.
There is some truth to that. If you get acquainted with ANE and Mediterranean religions, the idea that someone who has committed a crime, e.g. murder is a great example, is polluted, and so divine wrath of one or more gods will be pursuing them, and their pollution rubs off on other people, to the extent that if they are carrying such a person on their ship, they will also suffer, is a normal, typical belief for those religions. The sailors' actions make perfect sense in that religious milieu.
At the same time, the sailors are right - they are perishing because one of their gods is angry with someone onboard, and they need to deal with that person to appease that god. Yet here is a sacrificial substitionary atonement. Not because Jonah is innocent, but because he is guilty. I think I only realised the way that Jonah functions as a typology of Christ in this chapter by hearing and reflecting on Malcolm Guite's poem "The Christian Plummet". Go and read it, then come back.
https://malcolmguite.wordpress.com/2018/10/10/the-christian-plummet/
Guite is doing other things in this poem, including responding to Herbert's poem "Prayer", but I am interested in the simple way in which Jonah functions to go into the depths of the storm, to save his shipmates. In the Jonah narrative they are innocent (at least in this regard), even though we could find them guilty in many other respects; guilt or innocence is just not in view for them. But they are suffering under the tempest, and Jonah does get up and offer himself, he knows that God's wrath needs to fall on him for them to be saved, and so into the depths he goes.
So too, the good Lord. Though he is innocent, he knows that God's wrath needs to fall on him for the rest of this ship to be saved, and so he himself plunges into the depths of death. It is his outstretched arms that embrace the cold grip of the abyss. Those same "everlasting arms" that are "underneath", holding us up. There is no Jonah in the belly of the whale, without Jonah overboard. No three days in the ground, before six hours lifted up, no resurrection without the cross.