Muslim

Hadith Commentary: Benefits and Issues:
"Anta as-Salaam":
This means that You are free and pure from every defect and deficiency, from accidents and calamities, and from every kind of change and decline.

And "Minka as-Salaam":
This means that safety (salaam) is in Your hand; You decide safety for whomever You will and whenever You will, and for whomever You do not will, You do not decide safety.

And the purpose of Hazrat Aisha radi Allahu anha is that, generally, the Prophet sallallahu alayhi wa sallam would sit facing the qiblah and recite these words, and after that, he would turn his face towards the followers (muqtadis) and engage in the remaining remembrances and supplications, as is established from other narrations.

1339. Commentary: "So peace is upon You" — meaning, You are free from every kind of defect and imperfection, or You are the One who grants safety to people.

1512. English Commentary: The statement of Imam Abu Dawud rahimahullah pertains to the preceding chain of narration. And the words of the mentioned supplication are only as much as have been reported in authentic ahadith. As for those people who recite: (Ilaika yarji‘u as-salaamu wa adkhilna daar as-salaam tabaarakta rabbana wa ta‘aalaita ya dhal-jalaali wal-ikraam), this is not established by an authentic chain. Therefore, adding these words to the supplication of the Prophet sallallahu alayhi wa sallam is just like mixing water into pure milk, which is, in any case, incorrect—even if the water added is from Zamzam.

Benefits and Issues:
➊
This supplication should be recited after the obligatory prayer.

➋
The prescribed (masnun) supplication is only that which is mentioned in this hadith; the rest of the phrases are self-invented by people.
For example: (وَإِلَیْكَ یَرْجِعُ السَّلاَمُ، حَیِّنَا رَبُّنَا بِالسَّلاَمِ وَأَدْخِلْنَا دَارَالسَّلاَمِ)
Similarly, after (تَبَارَکْتَ), the words (رَبَّنَا وَتَعَالَیْتَ) are also added.
One should avoid these additional phrases.

➌
“The only amount of time they would sit” means that they would sit facing the qiblah for only that duration; otherwise, sitting for a long time for remembrance and supplications is established from the Sunnah. (Sahih Muslim, Al-Masajid, Chapter: Recommendation of Remembrance after Prayer and Its Description, Hadith: 594)