That very chain is likewise recorded by al-Bukhārī, al-Nasāʾī, al-Ṭaḥāwī, al-Bayhaqī (who cites it on al-Bukhārī’s authority), Aḥmad, and al-Dārimī.

The final additional detail is transmitted by Abū Dāwūd, al-Nasāʾī, al-Ṭaḥāwī, Aḥmad, and al-Bayhaqī through the first chain with a sound isnād that meets the criteria of the Two Imāms, and al-Bukhārī relates the same meaning elsewhere.

As for the middle addition, it comes through a different route from Ibn ʿUmar. Al-Bukhārī, al-Nasāʾī, al-Bayhaqī, and Aḥmad bring it by way of several chains from Sufyān ibn Sulaymān, who said:
“I heard Mujāhid report: Ibn ʿUmar—while he was at home—was told, ‘The Prophet ﷺ has entered the Kaʿbah.’ I hurried over and found that the Messenger of Allah ﷺ had already come out, with Bilāl standing between the two door-posts. I asked, ‘O Bilāl, did the Messenger of Allah ﷺ pray inside the Kaʿbah?’ He replied, ‘Yes, he prayed two rakʿahs between these two pillars,’ then pointed to the two pillars that lie on your left as you enter. He added, ‘After that he came out and prayed two rakʿahs facing the Kaʿbah.’”
This wording is Ahmad’s.

The clause mentioning “two rakʿahs” is also corroborated by Layth ibn Abī Sulaym and by Khuṣayf, both reporting from Mujāhid; Aḥmad records their versions as well.

Nor is Mujāhid the only one to narrate this from Ibn ʿUmar: ʿAbd Allāh ibn Abī Mulaykah corroborates it in the collections of al-Nasāʾī and Aḥmad, with a sound chain, and ʿAmr ibn Dīnār does so in an abridged form.