Simak bin Harb reported: I said to Jabir bin ahadeeth: Did you sit in the company of the Messenger of Allah (ﷺ) (may peace he upon him)? He said: Yes, very often. He (the Holy Prophet) used to sit at the place where he observed the morning or dawn prayer till the sun rose or when it had risen; he would stand, and they (his Companions) would talk about matters (pertaining to the days) of ignorance, and they would laugh (on these matters) while (the Holy Prophet) only smiled.
Hadith Referenceصحيح مسلم / كتاب المساجد ومواضع الصلاة / 670
Simak narrated on the authority of Jabir bin ahadeeth that when the Apostle of Allah (ﷺ) observed the dawn prayer, he sat at the place of worship till the sun had risen enough.
Hadith Referenceصحيح مسلم / كتاب المساجد ومواضع الصلاة / 670
Hadith Commentary:Benefits and Issues: Remaining seated in the mosque after the morning (Fajr) prayer until sunrise for the purpose of remembrance (dhikr), supplications (adhkar), and recitation (of the Qur’an) is a means of reward and merit. It is permissible to listen to and narrate pre-Islamic events or other historical incidents for the sake of admonition, exhortation, or taking lessons. Furthermore, while maintaining the sanctity and respect of the mosque, it is also permissible to laugh or smile therein when needed.
Source: Tuhfat al-Muslim: Commentary on Sahih Muslim, Page: 1525
´It was narrated that Simak bin Harb said:` "I said to Jabir bin Samurah: 'Did you used to sit with the Messenger of Allah (ﷺ)?" He said: 'Yes.' When the Messenger of Allah (ﷺ) had prayed fajr, he would sit in the place where he had prayed until the sun rose, and his companions would talk and remember things from the time of Jahilliyah and recite poetry, and they would laugh and he would smile.'"
Hafiz Muhammad Ameen
1359. Commentary: Sitting for the prescribed remembrances (adhkar) after the prayer is an agreed-upon matter. The imam should be even more diligent in this regard than others. In addition to the remembrances, after those prayers after which there are no emphasized sunnah (mu’akkadah) prayers—such as Fajr and Asr—it is appropriate for the imam to remain seated so that people may present their questions. In this way, the imam will maintain a connection with the general public, and will remain informed about general matters. Socializing with people in a pleasant manner is also an act of goodness. The remembrances after the obligatory prayer should be recited before the emphasized sunnah prayers. This is what is generally understood from the ahadith. As for the narration from Aisha radi Allahu anha that the Prophet sallallahu alayhi wa sallam would sit only for the duration of reciting the «اللَّهمَّأنتَالسَّلامُ……… الخ» supplication after the salam, what is meant by this is sitting facing the qiblah, not sitting in an absolute sense—that is, he would sit facing the qiblah for that duration, then turn towards the congregation. The Companions would only recite such poetry in his presence that was free from poetic nonsense. There is no harm in reciting good poetry in small amounts without establishing a formal gathering; however, it is not correct to hold formal poetry gatherings in the mosques. Excessive interest in poetry distances one from the Qur’an.
Source: Sunan Nasa'i: Translation and Benefits by Shaykh Hafiz Muhammad Amin Hafizullah, Page: 1359