I shall cite them, if Allah wills, in the place already indicated.
That said, the following hadith likewise proves the permissibility of praying there:
‘A’ishah, may Allah be pleased with her, said:
“I used to wish to enter the House and pray inside it. The Messenger of Allah ﷺ took me by the hand, led me into the Hijr, and said, ‘When your people rebuilt the Ka‘bah they reduced its original dimensions and left the Hijr outside the House. If you want to pray inside the House, pray in the Hijr, for it is part of it.’”
This report was recorded by Abu Dawud, al-Tirmidhi, al-Nasa’i, al-Tahawi—whose wording is quoted here—and Ahmad, through the chain of ‘Alqamah ibn Abi ‘Alqamah from his mother, on the authority of ‘A’ishah. Al-Tirmidhi graded it “hasan sahih.”
I add: The mother of ‘Alqamah is Marjānah, a well-known transmitter whom al-Taqrib describes as “acceptable.”
Her narration is corroborated by Safiyyah bint Shaybah, a well-known and reliable transmitter whose reports are included by the two Shaykhs.
Al-Nasa’i and al-Tayalisi also recorded a concise version that reads: “I said, Messenger of Allah, should I not enter the House?” He replied, “Enter the Hijr, for it is part of the House.” Its chain is sound according to the criteria of al-Bukhari and Muslim.