Grading: (2) Its chain is "feeble" (wahin) because of "Husam bin Missakk", whose weakness is agreed upon; he is "matruk al-hadith" (abandoned in hadith).
Reference / Source: Al-Bazzar (4338), al-Tabarani in "al-Mu'jam al-Kabir" (5119), Ibn 'Adi in "al-Kamil" (2/ 434), Abu al-Qasim al-Asbahani in "al-Targhib wa al-Tarhib" (268) and Ibn 'Asakir (10/ 461) recorded it through several routes from Yazid bin Harun, with this chain.

Reference / Source: Al-Tabarani recorded it in "al-Mu'jam al-Kabir" (5118) and "al-Awsat" (2851), and Ibn 'Asakir (10/ 461), by way of Sulayman bin Dawud al-Shadhakuni, from Sahl bin Husam bin Missakk, from his father, from Qatadah, from al-Qasim bin 'Awf al-Shaybani, from Zayd bin Arqam.
Technical note / Defect ('illah): In it the Successor is named as "al-Qasim bin 'Awf al-Shaybani", but Sulayman al-Shadhakuni is "matruk" (abandoned).

Reference / Source: Ibn Abi Shaybah (1/ 225) recorded it from Yazid bin Harun, from a shaykh of the people of Basrah, from al-Qasim bin 'Awf al-Shaybani, from Zayd bin Arqam.
Note / Clarification: So it occurs in the critical editions of Ibn Abi Shaybah's "al-Musannaf": with mention of al-Qasim bin 'Awf al-Shaybani, with the mention of Qatadah dropped, and with the Basran shaykh left unnamed. Al-Hafiz Ibn Hajar stated definitively in "Nata'ij al-Afkar" (1/ 308) that this shaykh is "Husam bin Missakk" himself, and said: "It is as if he left him unnamed because of his weakness."

Reference / Source: Abu al-Qasim al-Rafi'i recorded it in "al-Tadwin fi Akhbar Qazwin" (4/ 138) by way of al-Hasan bin Abi al-Rabi' al-Jurjani, from Yazid bin Harun, from Abu Umayyah al-Basri, from al-Qasim bin 'Awf, from Zayd bin Arqam.
Technical note / Defect ('illah): If al-Hasan al-Jurjani preserved it (reported it accurately), then most likely this "Abu Umayyah" is Isma'il bin Yahya (or Ibn Ya'la) al-Thaqafi al-Basri, who is "matruk al-hadith" and of no standing.

Corroborating chains and supporting reports: The statement "The mu'adhdhins will have the longest necks of all people on the Day of Resurrection" is narrated as "marfu'" from the hadith of Mu'awiyah bin Abi Sufyan (may Allah be pleased with him) in Muslim (387).

Corroborating chains and supporting reports: And from the hadith of Bilal bin Rabah (may Allah be pleased with him) himself in al-Bukhari's "al-Tarikh al-Kabir" (1/ 103), al-Bazzar (1365), al-Tabarani's "al-Kabir" (1080) and "Musnad al-Shamiyyin" (1888, 2141), al-Bayhaqi's "Shu'ab al-Iman" (2790), Ibn 'Asakir (3/ 106, 107) and Ibn Hajar's "Nata'ij al-Afkar" (1/ 308).
Details of the narration: Its wording is that Bilal said: "O Messenger of Allah, people trade and pursue their livelihoods, and we cannot do that." He (peace and blessings be upon him) said: "O Bilal, are you not pleased that the mu'adhdhins will have the longest necks of all people on the Day of Resurrection?"
Grading: Its chain is weak because some of its narrators are unknown (majhul) and some have softness (lin); despite that, Ibn Hajar declared it "hasan"!

Note / Clarification: There is disagreement over the meaning of "the longest necks of all people"; al-Hafiz Ibn Hajar cited eight views in "Nata'ij al-Afkar" (1/ 309). Among them is the view of al-Nadr bin Shumayl and Abu Dawud al-Sijistani that it means: people will be thirsty on the Day of Resurrection, and whoever is thirsty, his neck bends, whereas the mu'adhdhins will not be thirsty, so their necks will stay upright.

Note / Clarification: One of these views is that of Ibn Hibban, that "length" means their necks will be looking out in expectation of the reward. Another view is that the length is literal: because they used to stretch their necks when raising their voices in this world, their necks will be lengthened on the Day of Resurrection so that they are distinguished from others by it. It is also said: (their necks will be long) so that the sweat does not bridle them (i.e. so that they are saved from drowning in sweat).