I wonder if your question is just curiosity or if you have witnessed or heard verbalizations that make you wonder?
I'm a novice, but IMO most have no pain with normal egg laying. Each has their own patterns of verbalization before, during and after an egg is laid. I have witnessed one laying an egg while walking down the chicken ramp, one laying an egg while drinking at the water fount, and one of mine even layed an egg from the roost in the middle of the night ---and none even noticed they had laid those eggs
Some are quite verbal before they enter the nest, some go in silent. Some chatter in the nests. Most announce the egg after laying. Others announce and egg when someone else lays.
But I do agree some could be painful or at least uncomfortable with oversized eggs or eggs with large external calcium deposits. If a pullet/hen has irritation of the vent that also would likely cause pain. And an egg bound gal would certainly be in pain.