Mediator Dei repeats very traditional language in this teaching on the Eucharist. Keep in mind that this document was not addressed to laypeople, or even clergy and theologians, but bishops.
Trent was a reaction to the Reformation, and to the challenges laid down by Luther, Calvin, and others:
68. The august sacrifice of the altar, then, is no mere empty commemoration of the passion and death of Jesus Christ, but a true and proper act of sacrifice, whereby the High Priest by an unbloody immolation offers Himself a most acceptable victim to the Eternal Father, as He did upon the cross. “It is one and the same victim; the same person now offers it by the ministry of His priests, who then offered Himself on the cross, the manner of offering alone being different.”[Council of Trent, Sess. 22, c. 2]
The Church’s teaching on the Eucharist doesn’t begin with Trent. Pope Pius XII also cites Thomas Aquinas, of course, as well as one of the original Eastern doctors:
69. The priest is the same, Jesus Christ, whose sacred Person His minister represents. Now the minister, by reason of the sacerdotal consecration which he has received, is made like to the High Priest and possesses the power of performing actions in virtue of Christ’s very person.[Cf. Saint Thomas, Summa Theologica, IIIª, q. 22, art. 4] Wherefore in his priestly activity he in a certain manner “lends his tongue, and gives his hand” to Christ.[Saint John Chrysostom, In Joann. Hom., 86:4]
Christ is priest, yes, but also victim. Good Friday is recalled:
70. Likewise the victim is the same, namely, our divine Redeemer in His human nature with His true body and blood. The manner, however, in which Christ is offered is different. On the cross He completely offered Himself and all His sufferings to God, and the immolation of the victim was brought about by the bloody death, which He underwent of His free will.
Making s distinction between the cross and the altar of a church:
But on the altar, by reason of the glorified state of His human nature, “death shall have no more dominion over Him,”[Rom. 6:9] and so the shedding of His blood is impossible; still, according to the plan of divine wisdom, the sacrifice of our Redeemer is shown forth in an admirable manner by external signs which are the symbols of His death. For by the “transubstantiation” of bread into the body of Christ and of wine into His blood, His body and blood are both really present: now the eucharistic species under which He is present symbolize the actual separation of His body and blood. Thus the commemorative representation of His death, which actually took place on Calvary, is repeated in every sacrifice of the altar, seeing that Jesus Christ is symbolically shown by separate symbols to be in a state of victimhood.
This seems to be an involved symbolic interpretation of what was once a rather simple act of the Lord at the Last Supper, and a liturgical act of the early Church.