Upload files to WordPress with ajax via REST API

ajax.upload.js

var data = new FormData()

// Add data/files to formdata var

jQuery.ajax({
  url: wpApiSettings.root + 'routehere/v1/subroute/save',
  type: 'POST',
  beforeSend: function(xhr) {
    xhr.setRequestHeader( 'X-WP-Nonce', wpApiSettings.nonce );
  },
  data: data,
  cache: false,
  dataType: 'json',
  processData: false,
  contentType: false,
  success: (data) => {
    console.log('succes')
    console.log(data)
  }
})

rest.route.php

// For a GIST
add_action( 'rest_api_init', function () {

  // Register route
	register_rest_route( 'routehere/v1', '/subroute/save', array(
		'methods' => 'POST',
		'callback' => function ( WP_REST_Request $request ) {

      // Prepare array for output
      $output = array();

      // Request the data send
      $sendData = $request->get_params();

      // Identify user
      $user = wp_get_current_user();

      // Which user is logged in?
      $userID = $user->ID;

      // Get the upload files
      $files = $request->get_file_params();

      // These files need to be included as dependencies when on the front end.
    	require_once( ABSPATH . 'wp-admin/includes/image.php' );
    	require_once( ABSPATH . 'wp-admin/includes/file.php' );
    	require_once( ABSPATH . 'wp-admin/includes/media.php' );

      // Process images
      if (!empty($files)) {
        $upload_overrides = array( 'test_form' => false );
        foreach ($files as $key => $file) {
          $attachment_id = media_handle_upload( $key, $challengeID );
          if ( is_wp_error( $attachment_id ) ) {
            $output['status'] = 'error';
        		$output['message'] = '- The image could not be uploaded.';
            return $output;
        	} else {
            // Success
            $output['status'] = 'success';
            $output['message'] = 'File '.$attachment_id.' uploaded.';
        	}
        }
      }
      
      return $output;
    }
	));
});