Allamah Alusi (rahimahullah) has mentioned the following in Ruhul Ma’ani:
رأيت في بعض شروح البخاري ندب قراءتها عند رؤية الهلال رجاء الحفظ من المكاره في ذلك الشهر ببركة آيها الثلاثين
Is this established in the Hadith and will it be a recommended practice?
Answer
Translation of the above quote:
‘I have seen in certain commentaries of Sahih Bukhari that reciting it [Surah mulk] is recommended when sighting the new crescent, with the hope of being protected during that month through the blessing of the thirty verses of the Surah.’
I have not seen this mentioned in any Hadith.
The quote you have provided from Tafsir Ruhul Ma’ani also doesn’t state that it is from the Hadith.
It seems to be a prescription based on experience, since this Surah does have the effect of protecting its reciter. See here. Further, it consists of thirty verses. The logic behind this prescription is that since it has thirty verses, it is expected that its recital at the beginning of each month will protect the reciter for the thirty days of that month.
There is no harm in practicing this without considering it a sunnah. (Unless it can be traced from the Hadith)
One may also make the intention of practicing on the Hadith that recommends its recital every night.
And Allah Ta’ala Knows best,
Answered by: Moulana Muhammad Abasoomar
Checked by: Moulana Haroon Abasoomar