I asked Ayesha, Umm Muiminin, with what surahs the Messenger of Allah ﷺ would perform the witr prayer. She mentioned the same meaning, saying that in the third rakah he would recite "Say, He is Allah, the One" along with the two surahs of refuge.
حدثنا أحمد بن أبي شعيب حدثنا محمد بن سلمة حدثنا خصيف
سألت عائشة أم المؤمنين بأي شيء كان يوتر رسول الله ﷺ فذكر معناه قال وفي الثالثة بقل هو الله أحد والمعوذتين
Its chain of transmission is daif.Tirmidhi transmitted it, Witr, chapter on what has been narrated about what is recited in Witr, no. 463, and Ibn Majah, no. 1173, from the hadith of Muhammad bin Salama, with this chain. Tirmidhi said, hasan gharib, but its chain is daif, as Khaseef is a well-known daif narrator. The hadith has supporting narrations, except for the part mentioning the two Muawwidhatayn.