To what extent is the hadith reported on the authority of Abu Dharr al-Ghifari (may Allah be pleased with him) concerning a specific supplication and its merit authentic?

The hadith mentioned in the question was cited in the book Kanz al-Ummal, attributed to Al-Hakim Al-Tirmidhi in Nawadir al-Usul. This book, however, has been judged by scholars as weak in what it narrates uniquely. Therefore, this hadith is weak, and there is no evidence to support its authenticity.

Nevertheless, there is no harm in supplicating with it, without believing in the certainty of the reward mentioned therein. It is recommended to consistently recite the du'as (supplications) authentically transmitted from the Prophet, peace and blessings be upon him. Among the concise books that collect them is Hisn al-Muslim.