To what extent is what is narrated concerning the virtue of saying "Lā ilāha illā Allāh (There is no god but Allah)" upon waking up from sleep authentic, and does it entail not being questioned by the two angels in the grave?

There is no mention of anything that validates the correctness of the aforementioned matter. The greatest merit a believer attains is steadfastness during the questioning in the grave, and that is by strengthening faith and correcting one's creed. The Messenger of Allah, peace and blessings be upon him, said: "When a Muslim is questioned in the grave, he testifies that there is no god but Allah and that Muhammad is the Messenger of Allah. That is what is meant by His saying: {Allah keeps firm those who believe, with the steadfast word, in the life of this world and in the Hereafter}."