Is boycotting brothers who have withheld an inheritance considered one of the seven destructive sins, and what is the correct action in this situation?

Your right to inheritance is established, whether your father made a will or not. If he made a will to give his money to his wife and children to the exclusion of you, then this will is void, because it is a will made to an heir, and the Shari'a has forbidden that, as the Prophet, peace and blessings be upon him, said: "Indeed, Allah, the Blessed and Exalted, has given every rightful person his right, so there is no will for an heir."

You can take the matter to the courts to remove the injustice inflicted upon you. Severing ties of kinship is a grave matter and a major sin, but it is not among the seven destructive sins mentioned in the Prophet's hadith.