The Messenger of Allah ﷺ would not perform ablution after the ritual bath.
حدثنا أسود بن عامر قال حدثنا شريك عن أبي إسحاق عن الأسود
كان رسول الله ﷺ لا يتوضأ بعد الغسل
No references are available.
Its isnad is hasan. Abu Dawud reported it 1/65 no. 250, and Tirmidhi 1/179 no. 107, saying, hasan sahih. Both are in the chapter on purification. Nasai reported it 1/209 no. 430, and Ibn Majah 1/191 no. 579, both in the chapter on ghusl.