Referring to a quote by Edmund Bishop from 1899 [2, p45 note *]:
Apparently, many liturgists became so enthusiastic after the discovery of the Didache that they lost sight of reality. This led them to the most remarkable conclusions. Through their enthusiasm for the archaeological discoveries, they had lost the insight that the Faith and Doctrine can only develop to a deeper understanding in unity with the teachings of the Church Fathers through "organic growth" through the refutation of heresies. Moreover, this archaeological approach of searching for the pure source in order to reconstruct the origin of our Faith and the Holy Mass, respectively, intrinsically entails great risks. Namely that (aspects of) old heresies that had already been refuted and overcome in the past are now being reintroduced, because these "original sources" by definition potentially contain all these heresies from before their disappearance through the maturation process of "organic growth".
The "Liturgical Movement" in the 20th century like Fr. Adrian Fortescue (1917) [01], Fr. Anton Baumstark (1921) [02], Fr. Pio Parsch (1937) [03] and Fr. Joseph Jungmann, S.J. (1948) [04] generally described the H. Mass as a "Ordinary Synaxis of the (Christianized) Synagogue [01, p6, p70; 02, p43; 03, p44; 04, p392] / Last Supper, with the nucleus of the Eucharist proper [01, p54; 03, p18; 04, p11, p179; 05, p21] of which the origine form would have been a meal. This latter is mostly argued by their interpretation of the Didache. Herewith they did not refer to the essential links to the Old Testament Temple Cult. These discussions are more about (alleged) historical developments as founded on liturgical archeology searching for the origin as being the purest source of the Holy Mass. Especially this latter had led to a misunderstanding of the true distinction between the natural and supernatural orders, by which they went so far as to judge the correctness of the development guided by the Holy Spirit through the historical "Organic Growth". Indeed, all this critisism is then based on an amateurish archeology, in which they set aside the actual deepening of the Faith and the associated Devotional Practices, which have been preserved by the Holy Spirit throughout the ages by0 the refutation of heresies and the adoration of Christ in all aspects of how He has fulfilled the Law. It is this pride that resulted in their blindness to see the essence that "Christ was born to fulfill the Law and Prophets", and how that is connected to the fulfillment of the Temple cult of the Old Testament. Namely that Christ fulfilled the Law that regulates the Jewish Temple cult in its entirety, which also means that the Holy Mass is the fulfillment of the Old Testamentic Temple cult: the "Eucharist is a Sacrifice".
Without claiming to be complete an overview of the fulfilment is given here in its main points concerning the last week of Passion.
The fulfillment of the Law did not start with Christ hanging on the cross, Christ standing before the Sanhedrin, or Christ instituting the Eucharist at the Last Supper or something like that. Apparently, Christ's fulfillment of the Law refers to His entire earthly life, from conception to His death on the cross. Notice that Christ, the "Innocent Lamb of God", was born in the "Stable of David". This was the stable from which the lambs came to be sacrificed in the Temple. So, the "Innocent Lamb of God", was born in the "Stable of David" to be sacrificed in the Temple during Passover. However, Christ, the “Innocent Lamb of God” was then appointed by the “Children of Israel” as the “Scapegoat” to bear our sins, as at the associated Temple Feast of “Yom Kippur.” He was then led out of the city of Jerusalem as the “Scapegoat,” where He offered Himself on the cross for our sins and then rose from the dead because He was without sin. Thus, with the fulfillment of the two associated Temple Feasts of “Passover” and “Yom Kippur,” Christ, Priest in the order of Melchizedek, ultimately fulfilled the entire Law with the sacrifice of His Body for our sins on Golgotha (Lk 24:44-49) as the ultimate culmination. The Holy Mass can therefore only be associated with this ultimate culmination.
This fulfillment is therefore connected to the books of the Old Testament which proclaimed the Law. It therefore follows Exodus and Leviticus among others in its context of the "Exodus from Egypt, the land of slavery", which had a paradigm shift by its fulfillment to the "Exodus from the land of the slavery of sin".
Therefore, this process of fulfillment follows the Law as given in the Temple cult of the Old Testament. A rough outline of this fulfillment is given here with reference to the main points in the last week, the week of Passion, as follows:
Thus a "Holy Priesthood" who "offer spiritual sacrifices acceptable to God through Jesus Christ" (I Peter 2:5) during which the ordained priests "in Person of the High Priest, Christ" offers the Passover Lamb and then "in Person of the High Priest, Christ" eats and drink the Body and Blood of Christ,the Passover Lamb, as Sacrificial Meal, after which the faithful are invited as the "Holy Priesthood" to join the Sacrifice by eating the Body of Christ, the "Lamb of God". This is the one, true and eternal Sacrifice of the Eternal Passover Lamb, who is unblemished and appointed to be a "Scapegoat" and who is bearing our sins. In this way Christ used the context of the Passover as a Memory of the "Exodus from Egypt, the land of slavery" through the associated Feast of "Yom Kippur" for a paradigm shift into a remembrance of Christ as a memory of the "Exodus from the land of slavery to sin" of which He is the door to Heaven.
While the institution of the Eucharist by Christ at the Last Supper was on the Thursday evening. This Last Supper could therefore neither be a Sabbath meal, as suggested by the new Offertory prayers of the 1969 Reform, nor the Sacrificial Passover Meal of Pesach itself. While the Old Testament day is from sunset to sunset Thursday evening was one day too early for it. Rather, it was the first meal of the 14th day of the first month when the 7-day Feast of the Unleavened Bread began. Whereas the Unleavened Bread signifies being unblemished (I Cor. 5:7, I John 3:5, Hebr. 7:26) in contrast to the leaven bread that stands as the common symbol for Sin (Amos 4:5, Hosea 7:4, Lk 12:1, Matt. 16:6-12, Gal. 5:9, I Cor. 5:6-8). So, the Last Supper was the first Passover Meal at which the symbolic Unleavened Bread was eaten in the evening before the Sacrificial Passover Meal. It was from this meal that Christ used the symbolic Unleavened Bread and Wine for a paradigm shift into His innocent and unblemished Body and Blood. That is why Christ had to institute the Eucharist at the Last Supper by commanding the apostles, "Do this in remembrance of me".
With "Do this ..." He did not command them to repeat the Last Supper, but to repeat His Acts in union with and in remembrance of His Sacrifice on the cross as the ultimate climax of the fulfilment of the Law: "He took the Bread and blessed it", "He took the Cup and blessed it" (= Offertory: taking Bread and Wine from profane use to prepare them by offering it to our Lord for sacred use), then "He consecrated both, Bread and Wine" (= Consecration) with "the Remembrance" (= Anamnesis), after which "He broke the consecrated bread" (= Fraction) and finally "he gave to eat the consecrated bread and wine, his flesh and blood" (= Communion as the Sacrificial/Spiritual Meal). This all means that ". . . in remembrance of me" can only be the remembrance of Christ's fulfillment of the law in all its facets, how He has redeemed us. Herewith the Structure and Meaning of the Eucharist are fixed by Christ.
And as for the supposed connection with Synagogue services: apparently the apostles did not go to any of the many synagogues in Jerusalem. This raises the obvious question of how one can ever assume that synagogue service is more important than Temple Worship. Only when the apostles were outside Jerusalem did they first go to the Synagogues as the places where the Jews usually gathered. They prayed the prayers of the hours with the Jews and preached the gospel to convert them to Christ, as they did in the temple, "day by day" as they "were continually in the temple blessing God." It was precisely this effort to convert the Jews that led to their banishment from the Temple and the Synagogues (Acts 2:46; Acts 3:1; Acts 5:20,42; Acts 13:14-52; Acts 17:1-5; Acts 19:8-10; Luke 24:52-53). So, if their preaching in the Temple and the Synagogue was intended to convert the Jews, why should it be added to the Eucharist where the faithful were already converted? It is more likely, therefore, that the prayers at the beginning of the Holy Mass, the liturgical readings from the Gospel and the Epistles, as well as the preaching, should be considered as a preparation for the Sacrifice, which was developed under the guidance of the Holy Spirit.
Please note that the Synagogal services were rather new in the Jewish history. They were established after the return of the second Babylonian Exile and has therefore no direct reference to the Jewish Law and its fulfilment by Christ. It was Ezra, who after returning in Jerusalem from the Babylonian Exile, experienced that the Jews left in Israel had no or insufficient knowledge of the Torah and the Prophets and arranged studies by reading and preaching the Torah and Prophets outside the Temple (Neh. 8:5). From this example of Ezra these Synagogues were study houses for studying the Torah and the Prophets outside the Temple (Neh. 8:5), without any liturgical reading of the Torah and Prophets.
The institution of the Eucharist, therefore, does not refer to the Last Supper or the Synagogue Service, but as the fulfilment of the Old Testament Temple Cult the H. Mass is in its entirity the New Testament Temple Cult focussed on the Sacrifice of our Lord as the innocent Lamb of God bearing as Scapegoat our sins. As such, the Eucharist is the same true and eternal Sacrifice for our sins in which Christ ultimately fulfilled the entire Old Testament Temple Cult. Mystically, the Eucharist at the Last Supper, preceding the Crucifixion, as well as all those taking place since then at each H. Mass by Christ in His "Mystical Body" is one and the same as the physical Sacrifice at Golgotha, It is Christ, the Eternal High Priest, who offers and sacrifices Himself on the cross for our sins, a Sacrifice that still continues in our temporary conditions.