Is it necessary to perform Sa'i between Safa and Marwa after every Tawaf, whether it be obligatory or supererogatory?

Going between Safa and Marwah is not prescribed as a voluntary act. It is required of the pilgrim performing Hajj or Umrah only once, based on the words of Allah the Almighty: "Indeed, Safa and Marwah are among the symbols of Allah. So whoever performs Hajj to the House or performs Umrah, there is no blame upon him for circumambulating between them." It is not prescribed to perform it as a supererogatory act like Tawaf or prayer, because acts of worship are prescriptive.