What is the ruling on the prayer of one who believed he said, "My Lord, forgive me" before rising from prostration, then performed the prostration of forgetfulness, and was afflicted by the delusion of changing the intention of the prayer during it? Does his prayer become invalid if he thinks about the nature of the prayer during prostration?

Your prayer is valid even if you omit saying: "My Lord, forgive me," because it is a sunnah according to the majority of scholars. Even if the Hanbalis consider it obligatory, it is compensated for by the prostration of forgetfulness (sujud al-sahw), which you have performed. The cure for the whisperings (waswasah) regarding the intention is to disregard and ignore them. So, continue with your prayer and do not pay attention to these whisperings, and do not repeat the prayer no matter how frequent the whisperings become.