The Prophet ﷺ would not perform ablution after the ritual bath.
حدثنا إسمعيل بن موسى حدثنا شريك عن أبي إسحق عن الأسود
أن النبي ﷺ كان لا يتوضأ بعد الغسل
No references are available.
[Its chain is daif]. Ibn Majah also narrated it in the Book of Purification, chapter on performing wudu after ghusl, no. 579, from Ismail with the same wording. Ibn Sayyid an-Nas strengthened it, and Hakim graded it sahih according to the standard of the two Shaykhs, 1/153, and Dhahabi concurred with him. Abu Ishaq used an ambiguous form of transmission (anana).