Does the distinction between Qada’ and Ada’ in Niyyah apply solely to obligatory prayers? Do voluntary prayers like Salat al-Layl, when performed after Fajr, remain voluntary and not subject to Ada’ or Qada’, with the intention being Qurbatan ila Allah?
As obligatory Prayers have Adaa' when it is performed within its time, and Qadha; when it is performed after its time, recommended prayers also have Adaa' when it is performed within it's time, and Qadha when it is performed after it's time. Qurbatan ilallah is a condition in every worship, yet Adaa and Qadha should be in your intention.
Wassalam.