Set cacheability on a custom route returning XML

I'm working on fixing a custom module that returns XML from a certain route. Essentially what is described in the answers of this question.

Currently this route isn't being cached. I've tried to switch to using CacheableResponse and setting cache tags but received the error "The controller result claims to be providing relevant cache metadata, but leaked metadata was detected"

At this point I feel a bit lost. How can I adjust caching for this route so it's cached until the returned XML changes?

Here's my current response:

/**
 * Class CustomEntityFeedController.
 *
 * @package Drupal\my_module\Controller
 */
class CustomEntityFeedController extends ControllerBase {
    public function feed() {
        // Query for custom entities, loop through them, and build XML output.
        $xml = $xml_content_header . $xml_content . $xml_content_footer;
        $response = new Response();
        $response->headers->set('Content-Type', 'xml');
        $response->setContent($xml);
    }
}

So you did already manage to return a cacheable response object, otherwise you wouldn't be able to produce this error message. The cause of the error is bubbled-up metadata, for example from an entity query with access checks or from a rendered URL. For each, you find solutions by searching for the error message. If not, you can put the entire XML processing in its own render context. See How to get cache metadata from nested render array when returning response?

Instead of using a Response object, you need to use a \Drupal\Core\Cache\CacheableResponse object. The CacheableResponse class extends the Response class; it adds the addCacheableDependency() method can be used as in the following code.

$response = new CacheableResponse($user->label());
$response->addCacheableDependency($user);

What passed to addCacheableDependency() can be any object from which the cached data depends.