Should he continue to perform istinjāʾ after passing wind, a habit he has developed, given your fatwa that istinjāʾ is not required in this case and that his wuḍūʾ is valid, just like the wuḍūʾ of the Messenger of Allāh (peace be upon him)? What are the proofs for this? And is it established that the Messenger of Allāh (peace be upon him) commanded istinjāʾ after passing wind?

"Istinjāʾ" (cleaning oneself with water or stones) after passing wind is not legislated. It is a disliked act and an innovation (bidʿah) because there is no evidence for it in the Quran or Sunnah (definition). Furthermore, wind itself is not impure, nor is it accompanied by impurity. Your ablution (wudu') is valid and is not invalidated by performing istinjāʾ after passing wind.