How to include file attachment in ajax submission via the rest_api?

You can really use FormData just like you could use it with the old admin-ajax.php route, but:

1. Set processData and contentType to false.

2. Set the method to POST and make sure your REST API route supports the POST method.

   $('#create-book-form').submit(function (e) {
   
   //  var $this = $(this); // what's this?
       e.preventDefault();
   
       var data = new FormData( this ); 
   
       data.append( 'rtype', 'create' ); // add extra param
   
       $.ajax({
   
           url: BOOK_SUBMITTER.root + 'rfp-books/v1/books',
           data: data, //$.param(data),
           processData: false,
           contentType: false,
           method: 'POST',
           beforeSend: function ( xhr ) {
               xhr.setRequestHeader( 'X-WP-Nonce', BOOK_SUBMITTER.nonce );
           },
           success: function ( data ) {
               console.log( data ); // I added just for testing purposes.
           },
       });
   });
   

Then in your REST API endpoint callback, just use the $_FILES to get the uploaded file, e.g. $_FILES['file']. For other parameters, you can use $request->get_param(), e.g. $request->get_param( 'rtype' ).

Additionally or to other readers, you should have a file upload input in your form, e.g. <input type="file" name="file" />, but the name can be anything unless if you’re creating an attachment using the default wp/v2/media route.