Is the aforementioned transaction considered a sale of currency (بيع صرف) due to the lack of immediate possession in the same session, or a debt that can be repaid in another currency, knowing that the value is estimated?

This transaction is impermissible because it is a currency exchange (sarf) where the possession of one of the two countervalues is delayed beyond the contract session. If the types differ, then sell as you wish, provided it is hand-to-hand. Paper money takes the place of gold and silver, and is considered a currency type, with its types multiplying as the issuing authorities multiply. What you referred to, regarding the repayment of a debt with a different currency, is permissible if it was not agreed upon in the contract, provided that they do not separate while there is still anything between them, based on the Prophet's (peace be upon him) saying: "There is no harm in taking the price of its day, as long as you do not separate while there is still anything between you."