I was riding behind the Prophet ﷺ, and he continued reciting the talbiyah until he threw the pebbles at Jamrat al-Aqaba. He threw seven pebbles at it, saying takbir with each pebble.
أخبرني هارون بن إسحق الهمداني الكوفي قال حدثنا حفص عن جعفر بن محمد عن أبيه عن علي بن الحسين عن ابن عباس
كنت ردف النبي ﷺ فلم يزل يلبي حتى رمى جمرة العقبة فرماها بسبع حصيات يكبر مع كل حصاة
Its isnad is sahih. Ibn Khuzayma narrated it, no. 2881, 2887, from the hadith of Harun bin Ishaq, through him, and it is in Al-Kubra, no. 4085. Hafs is Ibn Ghiyath, and he stated explicitly that he heard it directly, as found in Bayhaqi, 5/137.