I know exactly how the Messenger of Allah ﷺ used to recite the Talbiyah, and I heard her recite it the same way afterward, "Labbayk Allahumma labbayk, labbayk la sharik laka labbayk, inna al-hamda wa al-nimata laka."
حدثنا محمد بن جعفر قال حدثنا شعبة عن سليمان قال سمعت خيثمة يحدث عن أبي عطية
إني لأعلم كيف كانت تلبية رسول الله ﷺ ثم سمعتها بعد ذلك لبت لبيك اللهم لبيك لبيك لا شريك لك لبيك إن الحمد والنعمة لك
Its isnad is sahih. Abu Atiya is Wadii, and he is trustworthy, his hadith appears in the Sahihayn. Sulayman is Amash, and he is well-known and trustworthy, his hadith is found with the group. The hadith was previously mentioned at 23922.