Is it permissible to recite the Quranic verses of "Al-Manazil" – as mentioned – during times of hardship and financial distress, by way of supplication?

It is not permissible to specify the recitation of particular verses from the Qur’an for a specific purpose unless there is a specific legal proof for it. The entire Qur’an is a blessing, a reward, and goodness. Claiming a specific effect for a particular verse—especially in relieving hardships and financial distress—requires proof. The Permanent Committee has issued a fatwa stating that reciting the Qur’an with reflection on its meanings, supplicating to Allah, and seeking refuge in Him are among the best and most legitimate acts of worship and closeness to Him. However, the specification mentioned in the question—distributing particular surahs to individuals for prayers for sustenance and the like—is an innovation (bid‘ah); because it has not been authentically reported from the Prophet, peace and blessings be upon him, nor from the Companions, nor from the imams of the Pious Predecessors. Goodness lies in following (the Sunnah), not in innovating, while supplication is legislated at all times and in all situations, and during prostration, at the end of prayer, and at the time of dawn.