In conclusion, the matter is exactly as al-Hāfiẓ al-ʿIrāqī summarized it:
The ḥadīth of Nuʿmān ibn Bashīr—“Supplication is worship”—was recorded by the compilers of the four Sunan and by al-Ḥākim. Al-Ḥākim ruled its chain sound, and al-Tirmidhī graded it ḥasan ṣaḥīḥ.

The report, “Supplication is the marrow of worship,” was narrated by al-Tirmidhī from Anas; he remarked, “It is singular from this route—we know it only through the narration of Ibn Luhayʿah.” Al-Suyūṭī deemed it weak in al-Jāmiʿ al-Ṣaghīr.

As for the ḥadīth of Abū Hurayrah, it was transmitted by Aḥmad and al-Tirmidhī, while Ibn Ḥibbān and al-Ḥākim authenticated it.

Glossary of terms
• Marrow (mukh) of worship: with a ḍammah on the mīm and a doubled khāʾ. Al-Miṣbāḥ explains that the mukh of a thing is its purest and most essential part. Thus, the “marrow of worship” means its quintessence and core, because it embodies obedience to Allah’s command, “Call upon Me.”

Points derived from the ḥadīths

1. The wording “Supplication is worship” proves that calling upon Allah is the very root of the devotion He has enjoined on His servants and for which He created them, as He says: “I did not create jinn and mankind except to worship Me” (51:56).
   The wording “Supplication is the marrow of worship” establishes that the purest, life-giving spirit of worship is to invoke Allah, for it fulfills His order, “Call upon Me.” When the seeker of need realizes that the success of his affairs rests solely with Allah, he cuts himself off from all others, singles Him out, and sincerely directs his supplications to Him alone.

2. Regarding the statement, “Nothing is more honored by Allah than supplication,” many noble texts convey this meaning, among them: “Your Lord has proclaimed, ‘Call upon Me and I will answer you’” (40:60), and, “When My servants ask you about Me, indeed I am near; I answer the call of the caller when he calls upon Me”