How do I set a Node's Paragraph field in a different language programmatically?
The paragraphs ERR field only contains one (pertinent) bit of info - the relationship to the paragraph entity. The field itself shouldn't be translated, because every time you set it, you're setting the paragraph for every translation of that node.
To provide translations, you translate the paragraph entity itself, e.g.
$node-&gt;field_images_descriptions-&gt;entity
  -&gt;addTranslation($lang_code, [
    'field_product_image' =&gt; $img[$key],
    'field_product_description' =&gt; $desc[$key],
  ])
  -&gt;save();