Is it disliked to establish projects such as building or buying a house or getting married in the month of Sha'ban, and does this affect their success, or is there no basis for that in the Sunnah?

This claim is false and falls under the forbidden practice of ṭiyarah (superstitious belief in omens), for the Prophet, peace and blessings be upon him, said: "There is no ‘adwa (contagion) and no ṭiyarah." Ṭiyarah is the act of being pessimistic about certain words, birds, people, days, or hours, which prevents a person from fulfilling their needs. It is obligatory upon the Muslim to believe that good and evil are in the hands of Allah and to rely on Him in all their affairs.