What is the ruling on paying off a debt to the General Organization for Social Insurance in installments, such that the amount paid in the end becomes double the original debt, knowing that the system does not allow for a reduction in the period for prompt payment?

If the insurance is compulsory and cannot be paid in cash, then there is no sin upon you. However, if it is voluntary, cooperative, and invested lawfully, then it is permissible to subscribe, and you are only required to pay the debt. If they increase the amount in exchange for deferment, that is usury (riba), and you must cancel the subscription. If it is commercial or invested in unlawful ways, then it is not permissible for you to subscribe if you have a choice, and you must cancel the subscription and withdraw your money.