What is the ruling on the prayer of one who forgot his ablution after exiting the restroom, with the strong presumption that he had performed ablution, and is his prayer valid?

The cure for obsessive thoughts (waswas) is to disregard them and pay them no attention. It is correct for the person suffering from waswas to act upon what they strongly believe — that they have performed ablution (wudu) — and to ignore mere doubts. Their prayer is valid, and they should continue to resist these obsessive thoughts until Allah grants them relief from them.