Modify your code as below:
/**********************************************
* Add featured video to REST API
***********************************************/
function add_featured_video_id() {
register_rest_field(
array('post', 'project'), 'featured_video_id',
array(
'get_callback' => 'get_featured_video_id',
'update_callback' => null,
'schema' => null,
)
);
}
Visit here, for more details on method register_rest_field
,