As I’ve been thinking about this post it strikes me that this whole incident isn’t really integrated with the rest of the book. As you say it never comes up that they know each other (except for the little thing about Mr. Elliot having heard of Anne) and afterward it kind of get’s put on the back burner while more interesting things are happening. I would assume Anne eventually told Lady Russell the story and that contributes to her “pain in understanding and relinquishing Mr. Elliot” and we learn that Fredrick helped Mrs. Smith recover her husband’s property in the West Indies. But, would anything have changed if Anne didn’t get this info about Mr. Elliot? He still would have gone away for a few days, Mrs. Musgrove and party would have come, Fredrick would have written his letter. It confirms that Anne was right not to trust Mr. Elliot but IMO it doesn’t really advance the story.