Is it obligatory to re-pray after discovering residue of nail polish on the nails after ghusl from menstruation, knowing that the prayer was performed with the intention of purification?

If the spot is merely a color that does not prevent water from reaching the skin, like henna, then it has no effect. However, if it has a physical mass and prevents water from reaching the skin, and you are certain that it is from the remnants of nail polish, then according to the majority of scholars, you must repeat the ghusl and the prayer. Whereas Shaykh al-Islam Ibn Taymiyyah holds the view that a small amount of barrier is overlooked. If you are not certain that it is from the remnants of nail polish and you doubt its presence at the time, then you are not required to repeat the ghusl or the prayer. If you are afflicted with obsessive whispers (waswas), then ignore them and act upon the opinion of Shaykh al-Islam for ease.