Praise be to Allah.
There is no tashahhud after Sujud as-Sahw because the Messenger of Allah (peace and blessings of Allah be upon him) did not do that, as is indicated by the sahih hadiths . If he had done that, he would have taught it to his Companions, they would have said so, and they would have narrated it to others. And he (peace and blessings of Allah be upon him) said: “Pray as you have seen me praying.”
Shaykh Ibn Qudamah said:
“Ibn Sirin and Ibn al-Mundhir said (concerning Sujud as-Sahw ): there is taslim [saying salam] in them but there is no tashahhud.
Ibn al-Mundhir said: the taslim [in Sujud as-Sahw ] is proven from more than one isnad, but there is some dispute concerning the tashahhud.” (Al-Mughni, 2/431, 432)
According to al-Nawawi, among the things we learn from the hadith of Dhu’l-Yadayn are:
“That Sujud as-Sahw was done at the time of the Prophet (peace and blessings of Allah be upon him).
That it consists of two prostrations, and that one should say Takbir (“Allahu akbar”) for each prostration. They are like the prostrations of prayer, because they are called sujud, and if they had been different, he would have explained that. One should say salam after doing Sujud as-Sahw , but there is no tashahhud, and if one has to do Sujud as-Sahw because of doing something extra in the prayer, this should be done after the salam.” (Sharh Muslim, 5/71)
And Allah knows best.