I know the common understanding is that Jonah waited, alive and conscious, in the belly of the whale until he was spat out.
Has a euphemized "children's version" become accepted truth? Perhaps we can set preconceptions aside for the moment and take a fresh look at this question. In the text and from what is naturally possible, chapter 2 may depict a pretty grim condition for Jonah.
Then Jonah prayed to the Lord his God from the belly of the fish, 2 saying,
“I called out to the Lord, out of my distress,
and he answered me;
out of the belly of Sheol I cried,
and you heard my voice.
3 For you cast me into the deep,
into the heart of the seas,
and the flood surrounded me;
all your waves and your billows
passed over me.
4 Then I said, ‘I am driven away
from your sight;
yet I shall again look
upon your holy temple.’
5 The waters closed in over me to take my life;
the deep surrounded me;
weeds were wrapped about my head
6 at the roots of the mountains.
I went down to the land
whose bars closed upon me forever;
yet you brought up my life from the pit,
O Lord my God.
7 When my life was fainting away,
I remembered the Lord,
and my prayer came to you,
into your holy temple.
8 Those who pay regard to vain idols
forsake their hope of steadfast love.
9 But I with the voice of thanksgiving
will sacrifice to you;
what I have vowed I will pay.
Salvation belongs to the Lord!”
10 And the Lord spoke to the fish, and it vomited Jonah out upon the dry land.
([Jonah 2, ESV][esv]; emphasis mine)
Deciding what type of writing Chapter 2 is may be helpful. Deciding when Jonah made this prayer may be helpful. Though your conclusion on whether Jonah is alive or not may have more influence on that question than the other way around. Is Jonah crying out from the belly of the whale (2:1) or from Sheol (2:2) or maybe in a way its both?
The presence of Sheol and Shachath (and some surrounding language) could be read as suggesting death.
Jonah 2:6 speaks of the pit, but that phrase using the word shachath for pit also translated "corruption" and is the same term used in Psalm 16:10
For you will not abandon my soul to Sheol,
or let your holy one see corruption (or the pit)
A nonreligious first reaction seems to be that it makes no natural sense that a man could survive in a whale three days, not without supernatural intervention. Should that be our starting understanding instead? Should we demand the text specifically show that he was kept alive rather than show that he died because his death would be the normal expectation?
Did Jonah actually die and, while dead or dying, cry out to God who heard him and resurrected him?
Also, given that Jesus later compares his death with Jonah's time in the fish, is it fair to say it means death for Jesus but not for Jonah?