What is the ruling on one who incorrectly completed a Prophetic Hadith and then regretted it, and is his action considered an intentional lie against the Messenger of Allah, may Allah bless him and grant him peace?

What you said is not considered intentional or unintentional lying. Rather, it is an excusable mistake, due to the Prophet, peace and blessings be upon him, saying: “Indeed, Allah has forgiven my nation for mistakes, forgetfulness, and what they are coerced into.” The warning mentioned in the aforementioned hadith is for those who intentionally lie about the Prophet, peace and blessings be upon him. As for the one who makes a mistake, there is no blame or sin upon him. It is advised to avoid this kind of thinking because it leads to obsessive doubts.