Is saying "صدق الله العظيم" (Allah the Almighty has spoken the truth) after reciting an ayah or ayahs from the Qur’an considered a bid‘ah (innovation), and if so, how did this phrase enter Islam?

Saying "Allah the Almighty has spoken the truth" after finishing a Quranic recitation is an innovation (bid'ah) because the Prophet, peace be upon him, and his Companions and the generation succeeding them did not do it. Some people's reliance on the verse, "Say: 'Allah has spoken the truth,'" does not apply here, because the verse was revealed to confirm the permissibility of food for the Children of Israel and is not a teaching to be recited after recitation. If it were so, Allah would have explicitly commanded it. As for believing in the truthfulness of Allah, it is an obligation. It is permissible to say "Allah has spoken the truth" when what Allah the Almighty has foretold comes to pass, confirming His word, just as the Prophet, peace be upon him, did when he saw Al-Hassan and Al-Hussein, recalling His statement, the Almighty: "Indeed, your properties and your children are but a trial."