Is it permissible for a person residing in Turkey, who is capable of working and supporting his family, to take humanitarian aid (food or money) distributed by organizations, knowing that it is not designated for the poor, but rather for all refugees?

If you are able to earn a living, you should investigate the aid. If it is zakat, then you have no right to it, according to the hadith: "Charity is not permissible for the rich, nor for one who is strong and healthy." However, if it is voluntary charity (sadaqat) and not conditioned for a specific group, then it is permissible for you to take it without asking, though it is preferable to refrain from it. Some jurists have definitively prohibited a rich person from asking for voluntary charity.