Is it permissible for a contracting company that works in building solar power plants to act as a subcontractor for building a solar power plant for an agricultural bank that engages in agricultural buying and selling activities, and has branches for Islamic transactions and other branches for usurious banking transactions? And in the case of impermissibility, is it possible to donate a portion of the profits to avoid embarrassment with the main contractor?

There is no harm in working on a solar energy project belonging to a bank that engages in some prohibited transactions, as long as your work does not directly involve something forbidden, nor does it provide direct or intentional assistance to it. This is because the default state of things is permissibility, and because the aforementioned bank's activities are not limited to usurious transactions but also include permissible activities such as managing agricultural businesses, and it has Islamic branches.