That the prosphora is leavened is not a detail of baking. In the middle of the eleventh century the use of unleavened bread by the Latin churches, the azymes, became one of the sharpest public grievances between Constantinople and Rome, argued alongside the papal claims and the addition to the creed in the exchanges of 1053 and 1054. It stayed in the polemical literature for centuries afterwards and it is still the most immediately visible difference between an eastern and a western altar.
The Greek argument was that risen bread is the proper sign of the risen and living Christ, that the church of the apostles used ordinary bread, and that a wafer without leaven imitates the Passover of the old covenant and so belongs to a dispensation that has passed. The Latin argument was that the supper was eaten at Passover, when no leavened bread was in a Jewish house, that unleavened bread is therefore what Christ himself used, and that the Latin churches had done the same from an early date. Each side could point at the gospels, which date the supper differently, and neither could settle the calendar question from the texts.
The Council of Florence addressed it directly in 1439 and declared that the body of Christ is truly confected in wheat bread whether leavened or unleavened, and that priests of each rite should follow the custom of their own church. That is where the doctrinal question rests, and it changed nothing about practice: the East still bakes leavened loaves and the Latin West still uses unleavened wafers, which is a reasonable illustration of how far a formal agreement and a living difference can coexist.