Did the Prophet (peace be upon him) prostrate and say "Astaghfirullah" three times after the tasleem of the prayer?

It is authentically narrated from the Prophet, peace be upon him, that when he finished the obligatory prayer, he would seek Allah's forgiveness three times, saying: "O Allah, You are As-Salam, and from You is peace; blessed are You, O Possessor of majesty and honor." The seeking of forgiveness was explained by the phrase: "I seek Allah's forgiveness, I seek Allah's forgiveness." It has not been authentically established from the people of knowledge that the Prophet, peace be upon him, would prostrate in this situation after the salutation. If it had been established, scholars would have transmitted it, and the great Companion Thawban, may Allah be pleased with him, did not mention it, despite mentioning the seeking of forgiveness, which indicates the impermissibility of this prostration.