Is there a tremendous decrease in suffering at stream-entry? Is it true that at stream-entry there is a profound decrease in the intensity of suffering perceived in samsara? If I'm not wrong, the Buddha does use the metaphor of a small clod of earth, as tiny as that can be picked up on a fingernail, to portray the amount of suffering one perceives after stream-entry, compared to the intense suffering, equivalent to the whole of earth, that a worldling feels in samsara?
You quoted the Nakhasikha Sutta which states that suffering that remains for a person who has attained stream entry is like dirt under the fingernail, compared to suffering remaining for an ordinary worldling which is equivalent to the great earth.
For e.g. a person's immediate family members all die due to an unfortunate accident. This person may become very depressed and stay depressed for a long time, if he is an ordinary worldling. He would experience sadness (aversion) and delusion - two of the three poisons.
A stream enterer would still become depressed, but then he will quickly come to his senses and remember the teachings of the Buddha, that all is impermanent.
He is aware that his sorrow is caused by clinging to the idea that the deceased family members belong to him (the self, an idea conjured by the mind).
He understands how the idea of the self arises, due to dependent origination. He understands how dependent origination works.
He also understands that the notion of persons and family members are all reification/ objectification-classification/ concept proliferation (papanca), just like the idea of the self.
The stream enterer would be able to let go a lot sooner than the ordinary worldling.
The ordinary worldling may get stuck in mental loops that amplify sadness and delusion. The stream enterer experiences sadness but has the wisdom to not get stuck in mental loops.
In comparison, an arahant will not suffer at all, because he has completely uprooted ignorance through wisdom. For the stream enterer, ignorance is still there, but it has been reduced greatly by wisdom.
The stream enterer still has craving and clinging, but now he has attained sufficient wisdom to understand them and how they work. In comparison, an arahant has completely destroyed craving and clinging.
Reduction of suffering for a stream enterer doesn't mean that negative events or painful sensations do not happen anymore. It simply means that the stream enterer does not suffer from them very much, compared to the ordinary worldling. His ability to endure them has increased tremendously.