What is the ruling on an engineer working in the design or supervision of the construction of towers that violate statutory height regulations? Is the money earned from this Haram? And does it become Halal if the owner pays a fine or a bribe?

Setting a height limit for construction falls under restricting what is permissible. The ruler has the authority to restrict what is permissible if there is a clear benefit in doing so. If the law serves a clear public interest or if violating it leads to a public harm, then it is not permissible to violate it or to cooperate with those who violate it, and the money earned from such an act is not lawful. As for paying money to neighborhood officials in exchange for overlooking the violation, this is a forbidden bribe and a major sin.