Is there any legitimate evidence from the Quran and Sunnah for the dislike of drinking at the end of a meal due to its causing illness, as opposed to its permissibility at the beginning and during it?

There is nothing in the Qur’an or Sunnah (definition) to indicate that drinking water during or after a meal is disliked. Rather, this is a matter transmitted by jurists from the perspective of ancient medicine, where it was established among physicians that it impairs digestion and causes ailments. Statements supporting this view have been reported from Al-Ghazali, Ibn Al-Jawzi, Ibn Muflih, Al-Mardawi, and Ibn 'Uthaymeen, who pointed out that the dislike is medical and ceases if drinking becomes a habit, or if the water is cold and the food is hot, as it would then be harmful. As for modern medicine, there is some disagreement on this matter.