Can we send additional data to Sentry?

As mentioned in the "USAGE" section of the README, you can use all the typical Sentry APIs with this module. Here are some examples from the Sentry docs:

\Sentry\configureScope(function (\Sentry\State\Scope $scope): void {
  $scope->setTag('page.locale', 'de-at');
  $scope->setContext('character', [
    'name' => 'Mighty Fighter',
    'age' => 19,
    'attack_type' => 'melee'
  ]);
}); 

Other Sentry APIs available to you include setting up an event processor (you can see how the various integrations included with Sentry SDK and Raven module do this).

In addition, for events captured thru Drupal logger, this module provides hook_raven_filter_alter() thru which Sentry events are passed, so you can use this hook to call methods on the \Sentry\Event that is about to be captured. We may need to improve the documentation a bit here :)