What is the ruling on working in a government institution that borrows with interest from banks to pay employee salaries?

As long as the work is permissible, the wage is lawful. The institution's borrowing with usury to pay salaries does not affect this; the sin falls upon those in charge of the institution, for the Prophet ﷺ said: "There will come a time upon the people when no one will remain but will consume usury. If he does not consume it, he will be afflicted by its dust."