Is it necessary to make up for fasting on Sunday, October 26th, a day on which one broke their fast in Qatar, given that Sunday marks the completion of the month of Ramadan in Egypt, and that the questioner will return to Egypt to spend the last days of the blessed month there?

You do not have to make up Sunday because you were a resident in Qatar, and the month was not confirmed there. Your ruling in Egypt is the ruling of its people, so you fast and break your fast with them, as the Prophet, peace and blessings be upon him, said: "The fast is the day you fast, and the breaking of the fast is the day you break your fast." If the month is confirmed in Egypt after twenty-nine days, then you must make up one day because you fasted twenty-eight days, and the month is not less than twenty-nine days.