(A ḥadith graded ḥasan ṣaḥīḥ—good and authentic.)
I say: It is sound through the first chain, whereas this particular route is weak because of the weakness of Zayd al-‘Ammī.
Al-Tirmidhī likewise cited it through the route of Yaḥyā ibn al-Nuʿmān, who said, “Sufyān narrated to us,” and he added:
They asked, “What should we say, O Messenger of Allah?” He replied, “Ask Allah for well-being in this world and the Hereafter.”
This additional wording is weak for two reasons: first, it comes through this deficient isnād; second, Yaḥyā ibn al-Yamān is the only one who reports it from Sufyān, whereas all the reliable narrators who transmit from Sufyān omit this addition.
Although Yaḥyā ibn al-Yamān is counted among Muslim’s narrators, he is described as having a poor memory. Al-Taqrīb states: “Ṣadūq, a devout worshipper, but he makes many mistakes and his condition deteriorated.”
3 – Via Ibrāhīm ibn al-Ḥasan al-ʿAllāf: “Sallām ibn Abī al-Ṣahbāʾ narrated to us from Thābit, from Anas.” Al-Khaṭīb recorded it through two chains from Ibrāhīm with this wording. I do not know anything about Ibrāhīm, and as for his teacher Sallām, Aḥmad judged his ḥadith fair, whereas others deemed him weak.