What is the ruling on working as an engineer in a bank that deals with both usurious and Islamic transactions, knowing that the work is limited to engineering supervision of projects funded by the bank and has no direct relation to financial matters?

If the tasks assigned to you at the bank belong to the Islamic branch and are carried out through Sharia-compliant contracts, then there is no objection to supervising them. However, if they are based on usurious contracts, then your supervision would be an aid to sin, which is forbidden by the Almighty's saying: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression."