Drupal has a method called isEmpty(). An example:
if($project->get('field_project_status')->isEmpty()) {
\Drupal::logger('my_module')->notice('Project '. $project->label() .' has no status yet.');
}
This is what it actually does:
public static function isEmpty(array $elements) {
return empty($elements) || count($elements) === 1 && array_keys($elements) === [
'#cache',
];
}
In twig you can use the following:
{% if content.field_project_status is empty %}
.. do your thing
{% endif %}
{% if content.field_project_status is not empty %}
.. do your other thing
{% endif %}