Grading: This hadith is "sahih". There is no harm in the men of this chain (la ba'sa bihim), except that there is disagreement from Qatadah regarding it: he narrated it sometimes as "marfu'" and sometimes as "mawquf".
Technical note / Defect ('illah): 'Umar bin Ibrahim (who is al-'Abdi) has been criticized specifically in his narration from Qatadah. There is also disagreement from him: sometimes it is narrated from him with mention of "al-Hasan al-Basri" in place of Sa'id bin al-Musayyab, but the correct version is with mention of "Sa'id bin al-Musayyab", as Shadh bin Fayyad and 'Abd al-Samad bin 'Abd al-Warith narrated it from him, since he has corroboration (mutaba'ah) for the mention of Ibn al-Musayyab, as will come.

Grading: A group of imams declared its being "marfu'" to be correct, among them Ibn Hazm in "al-Muhalla" (10/ 334), Ibn al-Turkumani in "al-Jawhar al-Naqi" (7/ 294), and Ibn Hajar in "Mukhtasar al-Bazzar" (1053). Al-Nasa'i also inclined towards strengthening it, as can be understood from his words after hadith (9086).
Important point: Moreover, even if its being "mawquf" were established, it would still have "the ruling of marfu'", because such a thing cannot be said merely from personal opinion. And Allah knows best.

Reference / Source: Al-Bayhaqi (7/ 294) narrated it from the author (al-Hakim), and said after it: He reported it thus as marfu', whereas the correct position is that it is the saying of 'Abdullah (bin 'Amr), not marfu'.

Reference / Source: Al-Khatib recorded it likewise in "Tarikh Baghdad" (11/ 112) through the route of 'Abdullah bin Hadir al-Baghdadi, from Shadh bin Fayyad.

Note / Clarification: And this narration will come later at number (7522) through the route of 'Abd al-Samad bin 'Abd al-Warith, from 'Umar bin Ibrahim, from Sa'id bin al-Musayyab.

Reference / Source: Al-Nasa'i (9087) and al-'Uqayli in "al-Du'afa'" (431) recorded it through the route of al-Khalil bin 'Umar bin Ibrahim, from his father, from Qatadah, from al-Hasan al-Basri, from 'Abdullah bin 'Amr.

Reference / Source: Al-Nasa'i (9086) and Abu al-Qasim al-Asbahani in "al-Targhib wa al-Tarhib" (1530) recorded it likewise through the route of Sarrar bin Mujashshir, from Sa'id bin Abi 'Arubah, from Qatadah, from Sa'id bin al-Musayyab.
Technical note / Defect ('illah): Al-'Uqayli reported it as "mu'allaq" (without the beginning of the chain), but in his mu'allaq narration he paired al-Hasan al-Basri with Sa'id bin al-Musayyab. We think this is nothing but an error (wahm) or a mistake by some copyists, because al-Nasa'i and Abu al-Qasim al-Asbahani mentioned only Sa'id, and we have not found the mention of al-Hasan al-Basri in Sarrar's narration. And Allah knows best. And Sarrar is "thiqah".

Corroborating chains and supporting reports: Sa'id bin Abi 'Arubah was matched in narrating this hadith as "marfu'" by "Hammam bin Yahya", in al-Bazzar (2349); and by "'Imran al-Qattan", in Abu al-'Abbas al-Sarraj's "Hadith" (593), al-Tabarani (14184), Ibn 'Adi (6/ 133), and Ibn 'Abd al-Barr's "al-Tamhid" (3/ 327).

Technical note / Defect ('illah): There is disagreement from "Shu'bah" regarding this hadith: Mu'adh bin Hisham narrated it from him as "marfu'", as will come with the author (al-Hakim) later at number (7523), whereas Muhammad bin Ja'far narrated it as "mawquf", as will come at number (7524), and likewise Yahya al-Qattan narrated it as mawquf, as in al-Nasa'i (9088).

Technical note / Defect ('illah): Likewise Hisham al-Dastuwa'i also narrated it from Qatadah as "mawquf", as al-'Uqayli mentioned, and he said: "This (being mawquf) is more likely correct."