Is it permissible for an employee responsible for following up on a company's projects to work on winning a project for the company to build a usurious bank, or to supervise its execution as a subcontractor?

It is not permissible to assist in a project for an interest-based bank, neither by follow-up, supervision, nor anything else, due to the Almighty's saying: "And do not cooperate in sin and aggression." If you excuse yourself to the company, explaining your religious point of view, then bear in mind Allah Almighty's saying: "And whoever fears Allah – He will make for him a way out And will provide for him from where he does not expect" and His saying: "And whoever fears Allah – He will make for him ease in his matter." As for the hadith (definition) "Purify your wealth with charity," it has no basis. Charity purifies its giver, due to the Almighty's saying: "Take, [O Muhammad], from their wealth a charity by which you purify them and cause them increase."