How to use addTranslation() on an entity's multi-value paragraph?
You have to loop over the multi-value field:
foreach ($lang_node-&gt;field_images_descriptions as $delta =&gt; $item) {
  $item-&gt;entity-&gt;addTranslation($lang_code, [
    'field_product_description' =&gt; $desc[$delta],
  ]);
}

$lang_node-&gt;save();