What is the story behind the verse of stoning (Ayat al-Rajm), and is it abrogated in wording but remaining in حكم (ruling), and what is the wisdom behind that?

The verse of stoning for the married fornicator was revealed as recited Quran, then its wording was abrogated while its ruling remained. This was a test for this Ummah and a demonstration of the extent of its obedience and its haste to sacrifice itself. As for the continuation of recitation despite the abrogation of the ruling, it is either to make known that the Quran is recited because it is the word of Allah, and thus one is rewarded for it, or to be a reminder of the blessing and the lifting of hardship.