What is the ruling on specifying the recitation of certain surahs a certain number of times—such as reciting Surat Al-Ikhlas 3626 times—to fulfill needs, knowing that this was not reported from the Prophet, may Allah’s prayers and peace be upon him, but rather transmitted from the imams and the righteous predecessors?

Reading a specific surah (definition) to fulfill a need or to earn a reward is a matter of tawqif (divinely ordained) and requires a legitimate proof, because establishing a reward and designating an act of worship for a specific matter can only be done through revelation. What has been reported from the Salaf and the Imams is to be examined: what has a legitimate basis should be acted upon, and what does not have a basis should be left; except for the Prophet, peace and blessings be upon him. No firm basis has been found for the example mentioned in the question concerning a Companion, a Tabi'i, or a famous Imam.