Ibn Ḥibbān, however, included him in al-Thiqāt (The Reliable Narrators). Ibn ʿAsākir gave him a biographical entry in Tarīkh Dimashq (History of Damascus) (14/381/2), but mentioned neither any criticism nor any accreditation of him. Thus, he is counted among the unknown narrators—if indeed he is not one of those who have been criticized.
As for the other matter, one cannot be confident that Ibn Ismāʿīl was Mūsā, for two reasons:
First, al-Ḥākim’s book contains numerous scribal corruptions in the names of its narrators, as is well known to those familiar with it. Therefore, where accounts conflict, its version carries less weight—as is the case here. In Ibn al-Sunnī’s narration, he is Muʾammal ibn Ismāʿīl, not Mūsā ibn Ismāʿīl.
Second, they did not list this Mūsā ibn Ismāʿīl among al-Ṣūrī’s teachers; rather, they listed Muʾammal ibn Ismāʿīl, as you have seen in al-Dhahabī’s remarks, and likewise in Lisān al-ʿAsqalānī.
From the foregoing, it is clear that the chain does not meet Muslim’s criteria, since Muʾammal ibn Ismāʿīl is not among Muslim’s narrators. Nor is it authentic, for Muʾammal had poor retention, as stated in al-Taqrīb; moreover, you already know al-Ṣūrī’s condition.
The hadith has also been narrated from Abu Hurayrah through another route, with the wording: “Whoever prays during a night, reciting one hundred verses, will not be recorded among the heedless; and whoever prays during a night, reciting two hundred verses, will be recorded among the devout and sincere.”
Al-Ḥākim recorded it (1/308–309) through Saʿd ibn ʿAbd al-Ḥamīd ibn Jaʿfar, who said: ʿAbd al-Raḥmān ibn Abī al-Zinād narrated to us, from Mūsā ibn ʿUqbah, from ʿUbayd Allāh ibn Salmān, from his father, Abu ʿAbd Allāh Salmān al-Agharr, from Abu Hurayrah, who said: The Messenger of Allah (peace and blessings be upon him) said—and then he cited it. He said: “Authentic according to Muslim’s criteria!” Al-Dhahabī agreed with him.
I say: Both of them were mistaken, for Muslim did not rely on Ibn Abī al-Zinād; rather, he narrated something from him only in the introduction. Furthermore, he was weak. Al-Ḥāfiẓ said: “Truthful, but his retention deteriorated when he came to Baghdad; and he was a jurist.”