Another explanation:

The Scholars of the Permanent Committee were asked: Is it prescribed for the worshiper to say "Allāhu Akbar" after the Tasleem before seeking forgiveness three times, based on the word "Takbeer" in the ḥadīth of Ibn Abbas, may Allah be pleased with them: "I used to recognise the end of the prayer of the Messenger of Allah ﷺ by the Takbīr" [agreed upon]? If this is not permissible, what is meant by Takbīr in the ḥadīth? Answer: "When the Prophet ﷺ concluded the prayer he would begin by seeking forgiveness three times and then say: 'O Allah, You are peace, and from You is peace, blessed are You, O Possessor of majesty and honor.' After that, he would proceed with the rest of the prescribed remembrances. As for the Takbīr mentioned in the ḥadīth, it refers to saying: سبحان الله، والحمد لله، والله أكبر thirty-three times each after the prayer, thus reconciling the various ḥadīths on the matter." [Fatawa of the Permanent Committee" (5/420)] Similarly, Sheikh Ibn Uthaymeen raḥimahullāh said: "The Prophet ﷺ would recite the Dhikr aloud after the prayer. 'Abdullah ibn 'Abbās, may Allāh be pleased with them, said: 'In the time of the Prophet ﷺ people used to recite the Dhikr aloud after the prayer.' He also said: 'We would recognise the end of the prayer of the Messenger of Allah ﷺ only by the Takbīr,' meaning the Takbīr that is part of the Dhikr, as these Adhkaar include saying 'Subhan Allah, Alhamdulillah, and Allahu Akbar.'" [Fatāwā Nūr 'ala Ad-Darb" by Ibn Uthaymeen (8/2), as per the Shamelah numbering]