Observing fasts in Shawwal is considered nafil, whereas qaza fasts are obligatory. In essence, both types of fasts hold separate importance.
While it is permissible to observe qaza fasts in Shawwal along with nafil fasts, it is important to note that if a person makes the intention to perform qaza for a missed fast while observing a nafil fast in Shawwal, the obligation to perform qaza will be fulfilled, but this fast will not count as a nafil fast.
Thus, it is recommended to observe the qaza fasts first in order to fulfil the obligation, and then separately observe the nafil fasts.