In a previous comment on Jonah, Scott Jorgenson said the following:
Well, as for me, I think the book of Jonah is a parabolical short story, a work of inspirational fiction to teach how God’s mercy extends beyond the borders of Israel to even the worst and most undeserving of enemies. I find that the book just reads far more naturally in that light; many interpreters including C. S. Lewis have thought so too. I’ve given several reasons for understanding the book this way previously, none of them original or idiosyncratic, and you can reference them if curious ("Narrative Theology" approach to Scripture - #50 by Relates).
So I find speculation about what really happened to the man Jonah while in the belly of the fish to be misplaced. What happened to him? Well, as the story says, the character Jonah prays elegantly, poetically and at length to God over the course of 3 days as he contemplates his fate, until God causes the fish to vomit him onto dry land; and nothing more of note (like a death and resurrection) takes place to Jonah over that period.
So I borrowed Robert Alter’s excellent translation and commentary on Jonah from the library as an ILL. So now I agree even more with Scott; the story is fabulous, not meant to be taken literally.