Is it permissible to pray the Shaf’ and Witr in congregation at home, and how do you explain Imam Malik’s starting with the obligatory prayer before the supererogatory prayer of Fajr, despite what has been established from the Prophet (ﷺ)?

Congregational prayer is permissible for the supererogatory prayers of Witr and Shafa'. If someone misses the Fajr prayer because they overslept and wake up after sunrise, they should first pray the obligatory (Fard) prayer. This is the well-known view among the Malikis. The Madhhabs of the Hanbalis, Shafi'is, Hanafis, and some Malikis hold that one should begin with the Sunnah (definition) of Fajr, then the Fard prayer. Imam Malik, may Allah have mercy on him, based his view on the authentic Hadith (definition) that commands making up the obligatory prayer immediately upon remembering it. Praying a Sunnah prayer would be a preoccupation from the obligatory prayer with something else. Furthermore, it did not reach him that the Prophet, peace and blessings be upon him, prayed the Sunnah of Fajr before the Fard prayer [in such a situation], as one is prohibited from engaging in anything other than the obligatory prayer when remembering it.