Is there any way to alter the response of JSON API module?
Please see how jsonapi_entity_base_field_info adds a computed property to the file entities. That should do.

If you don't want to create a virtual field, you can add a normalizer that only acts for that specific content type as a service. You'll need to use a higher priority than serializer.normalizer.entity.jsonapi (set to 21). Your custom normalizer can inherit from Drupal\jsonapi\Normalizer\ContentEntityNormalizer and add your custom stuff in getFields.