Is it obligatory to prioritize making up missed fasts (qada') over fasting the six days of Shawwal, knowing that qada' can be performed throughout the year, while fasting the six days is linked to Shawwal?

Scholars differ on the ruling of fasting the six days of Shawwal before making up for missed Ramadan fasts. The apparent view is that the basic Sunnah is achieved by fasting them before making up for missed fasts. However, the reward associated with fasting them after completing Ramadan is only attained by fasting them after making up for missed fasts, due to the Prophet's (peace be upon him) saying: "Whoever fasts Ramadan, then follows it with six days from Shawwal, it is as if he has fasted the entire year." Therefore, whoever missed any part of Ramadan has not fully fasted Ramadan.