Matthew 26:28
For this is my blood of the
new testament, which is shed for many for the
remission of sins.
You do not experience the remission of sins, which accompanies salvation, apart from the new testament/covenant.
And Jesus in those verses was speaking to Jews who the old covenant applied.
Christ linked the two inseparably.
2 Corinthians 3:6
Who also hath made
us able ministers of the
new testament; not of the letter, but of the spirit: for the letter killeth, but the spirit giveth life.
"Us", Believers in Christ who have experienced salvation, live under and and are minsters of the new testament/covenant.
"Us" are the Jewish apostles, Paul and Timothy, in 2Corinthians2:1 who were preaching to the Corinthians. Timothy had a Jewish mother, Eunice.
In the text, it is actually Paul speaking from the perspective of Jews who were part of the old covenant, and why he compared salvation in Jesus, to what they had been promised to them.
This can be seen in the natural of Paul's words....
2Corinthians 3:3 Forasmuch as ye are manifestly declared to be the epistle of Christ ministered by us, written not with ink, but with the Spirit of the living God;
not in tables of stone, but in fleshy tables of the heart.
....and in verse 7
7 But if the ministration of death, written
and engraven in stones, was glorious, so that the children of Israel could not stedfastly behold the face of Moses for the glory of his countenance; which
glory was to be done away:
The whole reference is that salvation in Jesus is the new covenant which God promised them who had the old covenant as promised in Jeremiah 31. The new covenant to the Jews became the gospel of salvation to the gentiles. Paul was sent to preach the gospel of salvation to the gentiles.
Acts 13:47 For so hath the Lord commanded us,
saying, I have set thee to be a light of the Gentiles, that thou shouldest be for salvation unto the ends of the earth.
1 Corinthians 11:25
After the same manner also he took the cup, when he had supped, saying, this cup is the
new testament in my blood: this do ye, as oft as ye drink it, in remembrance of me.
According to your claim, you do not need to partake of the Lord's Supper, because you were never part of the old covenant, and therefore since the Lord's Supper is a new covenant observance, it has no relevance to you (nor has it had for any Believer for the last 2,000 years).
Jesus was in the company of Jews at the last supper.
Taking part in the Lord's supper is done in similitude, in remembrance of Jesus. It is not because of covenant reasons. And it is not mandatory, because then it becomes works based salvation.