I assume that Montresor is not speaking his story aloud to anyone, including any confessor. The story looks like something that was written out on paper. There are too many details which a person speaking directly to another person would not be likely to include, especially fifty years after the fact. To take one of many possible example:
“Let us go, nevertheless. The cold is merely nothing. Amontillado! You have been imposed upon. And as for Luchesi, he cannot distinguish Sherry from Amontillado.”
How could Montresor quote Fortunato verbatim if he were speaking to another person extemporaneously?
I believe that Poe intended to have the reader assume that he, Edgar Allan Poe, had come into possession of a document, probably an old letter, which he had translated from a foreign language, most likely Italian, but possibly French or Latin, and was now publishing in a magazine. I assume that Montresor wrote a letter to a person whom he calls "You, who so well know the nature of my soul," and that the recipient kept the letter which was found among his papers when he died. Both Montresor and his confidant, or confidante, must have been quite old and close to death. Alternatively, Montresor might have written the letter one night when he was drunk but decided not to send it the next day when he was sober. (Some of us have done that ourselves, haven't we?) In that case the letter might have been found among Montresor's own papers when he died.
I do not believe that we are supposed to be listening to a long dramatic monologue, as is the case with Robert Browning's "My Last Duchess" and other such Browning poems, but are reading something that was putatively written by Montresor himself and then somehow came into the possession of an American editor named Edgar Allan Poe, who naturally would have had to translate it into English before he published it. Edgar Allan Poe may put his name on the piece because he is the owner, the translator, and the publisher--but not the author! That is Poe's fiction. The story is related to Poe's "Ms. Found in a Bottle." Edgar Allan Poe supposedly did not write the story: he found it in a bottle--or else somebody else found it in a bottle and passed it on to Poe.
Montresor would have been around forty when he murdered Fortunato. He says that fifty years have passed since that event. That would mean that he would be ninety when he told the story. He would probably be dead by the time it was published. If so, he could hardly be speaking it aloud--unless he is dead and is confessing to St. Peter!
I believe that Montresor supposedly wrote the confidential confession one night and that it survived on paper until it fell into the hands of Edgar Allan Poe. It was intended "for the eyes only" of one person. This technique makes it possible for the author to leave out a great deal of exposition. For example, there is no need for the author (Montresor/Poe) to say that the story is set in Venice. "You, who so well know the nature of my soul" knows where Montresor lives. I imagine the confidant, or confidante, to be living in France, since Montresor would be more likely to send a letter to France than to someone living nearby in Italy. That is the simplest explanation.