What should one who slept through the Fajr Adhan do if they woke up late after drinking water, and then the prayer was established?

The correct view is that whoever ate, thinking that Fajr had not yet dawned, and then it became clear that it had, there is nothing upon him. This is because he was ignorant of the time, and therefore excused, and his fast is valid. This is supported by the Almighty's saying: "Our Lord, do not take us to task if we forget or make a mistake," and the Hadith of Asma bint Abi Bakr, may Allah be pleased with them both, who said: "We broke our fast on a cloudy day during the time of the Prophet, peace and blessings be upon him, then the sun appeared." And the Prophet, peace and blessings be upon him, did not order them to make up the fast.