I say: Rūḥ and Muḥammad ibn Jaʿfar corroborated him, as you have seen; thus, through their route, the hadith is authentic according to the criteria of both al-Bukhārī and Muslim.
The hadith was also recorded by al-Bukhārī (4/223–224), Muslim (8/96 and 97), al-Tirmidhī (2/270), al-Dārimī (2/321), Ibn Mājah (4293), and Aḥmad (3/55–56), through other routes from Abū Hurayrah, attributed to the Prophet, with similar wording. Al-Khaṭīb also recorded it in al-Tārīkh (8/324) through another route from him. Al-Tirmidhī said: “A good and authentic hadith.”
Al-Tirmidhī has an additional wording: “If the believer knew the punishment that is with Allah, no one would hope for Paradise; and if the disbeliever knew the mercy that is with Allah, no one would despair of Paradise.” Muslim also recorded it (8/97). Both of them related it separately from the hadith, although their route is the same, unlike al-Bukhārī. Al-Suyūṭī confined its attribution to al-Tirmidhī alone. When al-Manāwī criticized him for this, noting that al-Bukhārī and Muslim had both recorded it, he claimed that the wording belonged to Muslim; but he was mistaken, for it is al-Tirmidhī’s wording, whereas Muslim’s wording differs from it slightly. Ibn Ḥibbān also recorded it (2523), and al-Bukhārī has something similar to it.
Muslim, al-Ḥākim (4/247–248), and Aḥmad (5/439) also recorded something similar from Salmān. Aḥmad (3/55) and Ibn Mājah (4294) recorded it from Abū Saʿīd al-Khudrī. Al-Ṭabarānī recorded an abridged version with similar wording, attributed to the Prophet, from Ibn ʿAbbās in al-Kabīr (3/145/1), but its chain of transmission is weak. Al-Haythamī said in al-Majmaʿ (10/214): “It was recorded by al-Ṭabarānī and al-Bazzār, and its chain of transmission is good.”