If you were not given a written or verbal quote for the faucet repair then there is room to argue that charge. The original quote there doesn’t look very formal so it probably didn’t have an implied pre approval for any changes.

At this point you might be able to call a plumber in the area and get a quote for fixing a leaky faucet and then tell your property manager the going rate is X and that is what you will pay since he didn’t quote you for the service

Last plumber I used was $250 plus parts and that felt expensive to me.