Must a Muslim complete reciting the Holy Quran in Ramadan? And is there a Hadith to support that?

The desirability of completing a full recitation (khatm) of the Quran in Ramadan (definition) is not an obligation but rather a recommended act. One who does not complete it does not incur sin, but misses out on many rewards. The Prophet, peace and blessings be upon him, used to review the Quran with Jibreel every Ramadan, and he reviewed it with him twice in the year of his passing. The righteous predecessors followed this guidance; some of them would complete the Quran every two or three nights in Ramadan, and some would complete it every night. The number of completions varies according to individuals and their circumstances. Whoever is engaged in contemplating the Quran or occupied with religious duties should recite in a manner that does not affect their understanding or work. As for one who is not in such circumstances, they should recite as much as possible without becoming weary.