What is the ruling on completing work to settle the dues of a contractor for a Riba-based bank, given that the engineer has not found another job and will be exposed to severe hardship if he leaves the work now?

Allah has forbidden assistance in haram (definition) in any form, as He, the Almighty, says: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression." Therefore, it is not permissible to work in the construction of an usurious bank, due to the assistance it provides in sin, and because the Prophet, peace and blessings be upon him, cursed the one who consumes Riba, the one who feeds it, its scribe, and its two witnesses, and said: "They are all equal" (reported by Muslim). It is well-known that the scribe and the two witnesses did nothing but assist.

It does not matter that your work is limited to settling the contractor's financial dues, because were it not for these dues, the contractor would not have undertaken the construction and would not have been able to complete it. The contractor buys what he needs and pays workers' wages through these payments. Therefore, you must immediately refrain from this work, unless there is an urgent necessity.