How can one overcome the exhaustion resulting from voluntary night prayers (Qiyam al-Layl) that leads to laziness regarding Fajr prayer and reading the Qur'an, and what was the guidance of the Companions in this matter?

Night vigil (Qiyam al-Layl) is among the best acts of devotion. Its time extends from 'Isha (evening prayer) until the appearance of dawn. It is preferable to perform it after some sleep, but if a person is unable to wake up after sleeping, then it is better for him to pray Witr before sleeping. The best guidance regarding Qiyam is the guidance of the Prophet (peace be upon him) and the prayer of David: he (David) used to sleep for half the night, pray for a third of it, and sleep for a sixth of it. One should not let one act of worship overshadow another, especially if the neglected act is superior and more beneficial than the performed one. The preponderant opinion is that congregational prayer in the mosque is obligatory, while Qiyam al-Layl is not obligatory. And the most beloved thing by which a servant draws near to Allah is what He has made obligatory upon him.