Start from a book they already loved
Every book's own page draws the books that sit nearest to it, with the reason written on each line.
The catalog already knows what sits beside a title: the same shelf, the same mood, the same appetite. Open a book they have loved and that page reads outward from it, each neighbour with its reason attached, so nothing has to be taken on faith.
What the page does not do yet is weigh one neighbour against another, or draw a map that begins anywhere other than a book we hold. This door starts where the catalog is strong.