I heard the Messenger of Allah ﷺ making talbiyah for both Hajj and Umra together, saying, "Here I am for Umra and Hajj, here I am for Umra and Hajj."
حدثنا هشيم أخبرنا يحيى بن أبي إسحاق وعبد العزيز بن صهيب وحميد الطويل
سمعت رسول الله ﷺ يلبي بالحج والعمرة جميعا يقول لبيك عمرة وحجا لبيك عمرة وحجا
Its isnad is sahih through its three paths. Yahya bin Abu Ishaq is Hadrami the grammarian, not Hinai.Bukhari related it, 3/422, no. 1563, in the Book of Hajj, chapter on Tamattu, and Muslim, 2/905, no. 1232, in the Book of Hajj, chapter on Ifrad and Qiran, both with similar wording, and Abu Dawud, 2/157, no. 1795, and Tirmidhi, 3/175, no. 821, who said, hasan sahih.