If a monster dies having already Swallowed Whole another creature, is the swallowed creature still subject to the threats that the stomach imposed while the creature was alive? I presume the swallowed creature is at least still grabbed until the monster is cut open or the creature Escapes, but are they also slowed 1? Do they need to worry about suffocating? Are they still taking the listed damage whenever they end their turn?
Yes. That is the main difference between Swallow Whole and Engulf: what happens to its victims when the creature dies.
I do note that with Swallow Whole, after the creature dies your allies can cut you out without any rolls needed.