If you have transferred your Borrowing History to your Completed Shelf, you can sort by clicking on the "Sort by” drop down menu, and you can filter using the options on the left side of the screen. You can add private notes about titles, or add tags that will help you filter your list. Searching is not currently possible, but sorting and filtering are helpful.
Exporting is not currently available from your raw Borrowing History list or Completed Shelf, but your reading history can still be exported from your account in Classic Catalog.
In addition, while you are searching the catalog, you will see an indication that a title is on your Completed Shelf, so you’ll know what you’ve read without having to check your history: