I would like to use the API or SEDE to discover which of my shared links (created by the "share" button as appears below each question/answer) have been visited by the most unique IP addresses.
Which table is this information stored in? I tried searching data.stackexchange.com/stackoverflow/queries for visits, hyperlink, link, etc. and it looks like no one has created this query yet.
You cannot do this. Reference this, barely upvoted, feature request from six years ago.
That information is not available in the API, SEDE or the Data Dump.
You can see this by reviewing:
user
object, which is a likely place for a pointer to such information