What is the ruling on prayer if someone, in the final Tashahhud, unintentionally adds "He is One, without partner; sovereignty and praise belong to Him, and He has power over all things," and does not perform the prostration of forgetfulness (sujud al-sahw)?

It appears you added an extra verbal element to the Tashahhud by mentioning a prescribed remembrance in an improper place. Your prayer is valid, and you do not need to repeat it. Scholars differ on whether prostration of forgetfulness (sujud sahwi) is required in this case. According to the view that it is prescribed, it is supererogatory (mustahabb), and omitting it does not invalidate the prayer.