Is it permissible to pay the bank after the governorate has transferred the debt to it and started collecting installments from it, knowing that the unit price doubles with installment payments and the installments increase annually, and is this considered a usurious loan?

If the bank purchases residential units and sells them by installments, it is permissible to buy from it, provided that the Shariah guidelines for installment sales or Murabaha for the one who commands the purchase are adhered to. However, if the units are owned by the Governorate and the debt will be transferred to the bank, this is not permissible Islamically, because it is selling a debt to someone other than the debtor, which is forbidden due to its inclusion of riba al-fadl (excess interest) and riba al-nasi'ah (interest due to delay). If the contract was made with the Governorate without knowledge of the debt transfer, then the contract is valid, and the sin falls upon the Governorate and the bank.