Is the aforementioned transaction, in which dollars are converted to dinars via an intermediary website, and then I am notified of the transferred amount two days before receiving it, considered Riba al-Nasi'ah (usury of delay)? And can electronic notifications be considered constructive possession, or is the nature of the transaction described as an agency and not currency exchange?

There is no harm in the website transferring your balance from dollars to you via a bank or reputable financial institutions, so that it reaches you in dinars. This is because the website acts as your agent, and its receipt of proof of transfer from the bank takes the place of actual possession.

It is permissible to exchange different currencies, even if they differ in quantity, provided that possession takes place in the same session. The receipt of a check or transfer slip is considered constructive possession. It is also permissible to conduct a bank transfer in a currency different from the amount provided by the transfer applicant. This consists of an exchange with actual or constructive possession, followed by a transfer of the amount in the purchased currency.

The delay in your ability to withdraw the money for the period customary among banks does not cause harm, as the delay in bank crediting is excused in a way that allows the beneficiary to take actual possession within the periods customary in transaction markets.