What is the ruling on the youth housing system in Egypt, in which an upfront sum is paid, the state subsidizes a portion, and the bank pays the remainder, then the young person pays the price in annual installments with an increase of 7.5%? And is this transaction considered a loan or an installment sale?

This loan is explicit usury (riba) and not an installment sale, because the bank pays the remainder of the unit's price and then demands repayment with an increase over what it paid, and that is the forbidden usury. However, if the residential units were owned by the bank, or if the bank purchased them from their owner and they came into its possession, and then it sold them in installments, there would be no objection.