What is the ruling on Quranic verses published on social media that do not begin with "Bismillah" nor end with "Tasdiq"? And what is the ruling on the one who publishes them?

There is no disagreement regarding writing the Basmala at the beginning of all surahs of the Qur’an except Surah (definition) At-Tawbah (definition). As for writing it before every verse, we do not know of anyone among the people of knowledge who mandated that. This is clear from the Prophet's (peace be upon him) letter to Heraclius, where he did not write the Basmala before the verse. As for saying "صدق الله العظيم" (Allah the Almighty has spoken the truth) after writing something from the Qur’an or reciting it aloud, it is not from the Sunnah (definition).