Is adding the phrase "for me and my parents" when supplicating with "My Lord, forgive me, have mercy on me, grant me well-being, provide for me, and guide me" between the two prostrations considered an innovation (bid'ah)? And if not, what is the difference between that and not adding the word "wal-shukr" (and gratitude) when rising from bowing?

A worshiper should not persistently add the phrase "and for my parents" in the supplication between the two prostrations, or the word "and gratitude" in his praise after bowing, because this has not been authentically reported from the Prophet, peace and blessings be upon him. However, he may supplicate for his parents in his prostration and after his tashahhud. What is prescribed for the supplication between the two prostrations is: "O Lord, forgive me, O Lord, forgive me," or "O Allah, forgive me, and have mercy on me, and grant me well-being, and guide me, and provide for me," or "and جبرني (compensate me)" instead of "and grant me well-being."