When Paul wrote this first reading from Ephesus in the year 56 twenty-three years after the Last Supper the people were still celebrating the Eucharist at a full meal the way they had at the Last Supper. Paul’s letter deals with the disturbances of such a gathering of poor and rich.
In recent centuries the Church has been associating the Mass so closely with the death of Jesus on the cross that we have gotten away from Paul’s way of referring to the Mass as “The Lord’s Supper.” I notice the switch away from emphasizing the Last Supper by the way some priests put a crucifix before them on the altar at their Masses.
Of course, Our Lords sacrifice was completed on the cross, but it very much had its beginning at the last Supper.
The prayer that Jesus uttered at the Last Supper was a sacrificial prayer that culminated in our joining Jesus offering ourselves with him in the Pleasing Gift of a complete sacrifice.