Does divorce occur if I swore to my wife—at her request—that I had deleted a specific application from the phone, but then I only hid it and did not delete it, knowing that my intention was not divorce, and that I know that swearing by divorce, if intended only as an oath, necessitates an expiation for breaking an oath (kaffarat yamin) upon breaching it?

What we understand from your question is that your wife asked you to swear by divorce to delete an application, so you hid it and did not delete it. Then you swore by divorce, falsely claiming that you had deleted it. In this case, your wife is divorced from you, and you may take her back before the expiration of her waiting period, provided this divorce does not complete the three divorces.

If you did not swear falsely, but rather intended something true with your oath, while your wife understood something else, then in this case, you have not broken your oath, your divorce has not occurred, and no expiation for an oath is binding upon you, because intention is considered in an oath.