Is it permissible for the ship's captain to take a 10% commission from the value of the ship's monthly provisions, a practice that is globally customary and given without request, and without it affecting the quality of the provisions or the continuity of the dealings?

You must inform the authority responsible for the amount paid by the supplier. If they permit you to take it, then it is permissible. Otherwise, you must return it to them, because you are a trusted agent for them, and that commission is their right. It has been authentically reported from the Prophet, peace and blessings be upon him, that gifts to workers are forbidden, and that whatever is taken in addition to the determined wage is an act of betrayal (ghulūl).