Is the project manager's approval of the new price submitted by the contractor permissible, given that the supervisor in the company tried to raise the price to benefit from it, and that the contractor will not give the supervisor any part of this amount because he believes it is unlawful?

It is incumbent upon the supervisor to be faithful to his company, and he is not permitted to defraud it. As for you, it is incumbent upon you to abandon relying on the inflated price. Whoever contravenes the religiously mandated advice has committed an error. Advice is obligatory for Muslims and non-Muslims alike. Therefore, you must advise the company manager by informing him of the price increase. If he approves it, then it is permissible for you to benefit from the increase; otherwise, you must return it to him. What you did by dealing directly with the project manager is the correct course of action to prevent the supervisor from taking what he does not deserve.