I bypassed the Catch Updated plugin (deactivated it, actually), but unfortunately I was still unable to upload the theme.
The “Upload Theme” button on the theme install page is not working. In fact, nothing on that page works. No featured themes appear, no popular themes, the latest, etc. Nothing happens when those options are clicked, either.
Since it seems I can’t include a screenshot, I have included a link to one instead This is a screenshot of the install theme page: