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.

Did you get a quote, agree to the service, and have the service completed? Then you probably don’t have much you can do. He’d probably take you to small claims court and win. The only possible save is you being in the military and out of country.

Did you pay too much? Yes. Is he taking a cut? Yes. Is any of that illegal? No.

Unless the work wasn’t actually necessary or completed. Do you suspect either?