Investigate moving to WP core's AJAX uploader

We're currently packaging and using `jquery.fileupload.js` and `jquery.iframe-transport.js`. Both packages are significantly out-of-date. It appears most of the exploits for the packages have been with the PHP side of things, but it might be worth investigating if we can use WP core's built-in packages to accomplish the same functionality.

If we can't easily do that, let's [update that library](https://github.com/blueimp/jQuery-File-Upload) and update our implementation as-needed.

Start by locating how jquery.fileupload.js and jquery.iframe-transport.js are packaged and used, then compare that implementation with WordPress core's AJAX uploader. Check whether core can provide the same functionality; done means documenting that decision and either migrating the implementation or updating the linked blueimp/jQuery-File-Upload library as needed.

Written by the indexing model from the issue text.