Custom endpoint that returns an xml

By default, the output returned by your endpoint/callback will always be sent as a JSON-encoded string (and the Content-Type header would also be/contain application/json), so you can’t use that callback for sending an XML feed.

However, you can use the rest_pre_serve_request hook if you want your REST API route to serve a different type of content like the XML feed in your case.

So for example, you can do:

1. Set your callback (smg_feed()) to return the XML data which will be echoed in the maybe_smg_feed() below: (note that the permission_callback should always be set, check the REST API handbook for more details)

   function smg_feed( $request ) {
       // ... your code ...
       return 'your XML data';
   }
   
   add_action( 'rest_api_init', function () {
       register_rest_route( 'smg/v1', 'feed', [
           'methods'             => 'GET',
           'callback'            => 'smg_feed', // make sure it returns an XML string
           'permission_callback' => '__return_true',
       ]);
   });
   

2. Then send the XML response like so:

   function maybe_smg_feed( $served, $result, $request, $server ) {
       // Bail if the route of the current REST API request is not our custom route.
       if ( '/smg/v1/feed' !== $request->get_route() ||
           // Also check that the callback is smg_feed().
           'smg_feed' !== $request->get_attributes()['callback'] ) {
           return $served;
       }
   
       // Send headers.
       $server->send_header( 'Content-Type', 'text/xml' );
   
       // Echo the XML that's returned by smg_feed().
       echo $result->get_data();
   
       // And then exit.
       exit;
   }
   add_filter( 'rest_pre_serve_request', 'maybe_smg_feed', 10, 4 );
   

Alternatively (as I mentioned in the original answer), without using the REST API (which does work), you can use add_feed() to deliver the XML feed.

( PS: Thanks to @TimothyJacobs for his help/comment. 🙂 )