Does the husband's informing his wife of his acceptance of divorce after treatment with Ruqyah Shariah—despite his actual unwillingness to do so—contradict the rulings of Islamic Shariah?

Lying is a major sin, but it is permitted out of necessity or for a preponderant benefit.

It is narrated in the Sahihayn (Bukhari and Muslim) that the Messenger of Allah (peace be upon him) said: "Indeed, truthfulness leads to righteousness, and righteousness leads to Paradise. A man keeps on telling the truth until he becomes a truthful person. Indeed, lying leads to wickedness, and wickedness leads to the Fire. A man keeps on lying until he is written before Allah as a liar."

However, Islamic law has permitted lying in a few matters where a greater benefit outweighs it, and this includes what a man says to his wife or what a woman says to her husband. Therefore, there is no sin upon you if you promise your wife what she desires, such as divorce or other things, for the sake of her treatment and an attempt to reform her. You are not obligated to fulfill what you promised her.