Unable to add newly created term to the node

I want to add new taxonomy term to group of nodes that have specific terms already.

To retrive them I use this function

function getNodesByTaxonomyTermIds($termIds){
    $termIds = (array) $termIds;
    if(empty($termIds)){
      return NULL;
    }
  
    $query = \Drupal::database()->select('taxonomy_index', 'ti');
    $query->fields('ti', array('nid'));
    $query->condition('ti.tid', $termIds, 'IN');
    $query->distinct(TRUE);
    $result = $query->execute();
  
    if($nodeIds = $result->fetchCol()){
      return Node::loadMultiple($nodeIds);
    }
  
    return NULL;
  }

then in foreach loop I'm adding im adding them to new term based on their creation date but adding does not work.

Here is my field structure:

Firstly I tried all of those:

$node->set('field_news_categories', ['target_id' => $termID])
$node->set('field_news_categories', $termID)
$node->set('field_news_categories', array($termID))
$node->field_news_categories->setValue(['target_id' => $termID])
$node->field_news_categories->setValue($termID)
$node->field_news_categories->setValue(array($termID))

none worked so I thought maybe I should pass whole field with exact same structure, so I wanted to get field and just append the id and then pass it as argument in set method, but I wasn't able to get field either. All I was receving were null values or empty arrays. I tried:

$node->field_news_categories->getValue()
$node->get('field_news_categories')->getValue()
$node->field_news_categories->value
$node->get('field_news_categories')->value
$node->field_news_categories
$node->get('field_news_categories')
$node->get('field_news_categories')->target_id
$node->get('field_news_categories')->entity
$node->get('field_news_categories')->referencedEntities()

Project is in drupal 9

To append an entity reference item use:

$node->field_foo[] = ['target_id' => 123];

And as Kevin noted in the comments, make sure you save the entity.

$node->save();