Has it been reported from the Salaf that reciting the three Surahs (Al-A'la, Al-Kafirun, and Al-Ikhlas) in Witr prayer is only prescribed if the three rak'ahs are prayed consecutively, and not if they are separated?

It has been authentically established that the Prophet, peace and blessings be upon him, used to pray Witr with three rak'ahs, both connected and separate. The evidence for this is that there are two ways to pray Witr with three rak'ahs: either by performing them continuously (sardan), or by making taslim after two rak'ahs. If he prayed Witr with three rak'ahs, he would recite "Glorify the Name of your Lord, the Most High" in the first rak'ah, "Say, 'O disbelievers!'" in the second, and "Say, 'He is Allah, [who is] One'" in the third. There is a difference of opinion regarding the addition of the Mu'awwidhatayn (the last two surahs of the Quran) in the third rak'ah.