Is borrowing from a bank with usurious interest to buy a large apartment considered an urgent necessity that permits the forbidden, or does it remain forbidden, requiring the sale of the car to repay part of the loan as expiation for the sin?

Borrowing from banks with interest is the usury (riba) of Jahiliyyah (pre-Islamic era) which is forbidden. Purchasing a house is not considered a necessity that permits riba, because the need for housing can be met by renting. It is obligatory to repent to Allah for this great sin and to resolve not to return to it. The sooner you repay the loan, the better, but it is not necessary to sell your car to pay off part of it.