Is it permissible for me to work as a design engineer for industrial control panels for contractors who obtained government projects through unlawful means (bribes or favoritism), and is the money earned from this work permissible, knowing that my work is purely technical and I have no involvement in how the contractor obtained the projects?

Your agreement with the contractor to perform project work is not problematic, especially if you are unaware of his circumstances or whether he engaged in fraud or offered a bribe. You are not obligated to investigate that. If you come to know that he offered a bribe or committed deception, advise him to repent. However, it is not impermissible for you to work with him, because your work is separate from the way the project came to him.