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It seems that the Catholic Church sees baptism as entering into covenant, resulting in the baptized incurring baptismal promises to keep for the rest of their lives. The covenant is the New Covenant, see CCC 1267:
1267 Baptism makes us members of the Body of Christ: "Therefore . . . we are members one of another." [Eph 4:25] Baptism incorporates us into the Church . From the baptismal fonts is born the one People of God of the New Covenant, which transcends all the natural or human limits of nations, cultures, races, and sexes: "For by one Spirit we were all baptized into one body." [1 Cor 12:13]
This 2020 article by Rev. David Justin Lynch from Saint Cecilia Catholic Community explains baptism as covenant, compares it to various OT covenants, considers the purification motif of OT baptism applied to Catholic teaching that baptism removes the effect of original sin, connects the reception of the Holy Spirit in baptism with what happened in Jesus's own baptism, talks about baptism as our anointing to become prophet, king, and priest like Jesus, etc.
If you are wondering how the Catholic Church regards the relevance of the OT covenants for the Jewish people today, you maybe especially interested in the series of documents the Catholic church has issued in the past 50+ years regarding God's relationship with the Jews, effectively softening the Supersessionism view as well as how we as the New Covenant people of God should regard them with gratitude. This article is an excellent introduction for the topic, commenting the latest 2015 document "THE GIFTS AND THE CALLING OF GOD ARE IRREVOCABLE" (Rom 11:29) A Reflection on Theological Questions Pertaining to Catholic-Jewish Relations on the Occasion of the 50th Anniversary of “Nostra ætate” (No. 4).
Quotes from the article commenting on the document:
That his will for salvation is universally directed is testified by the scriptures. Therefore there are not two paths to salvation according to the expression 'Jews hold to the Torah, Christians hold to Christ'. Christian faith proclaims that Christ’s work of salvation is universal and involves all mankind. God’s word is one single and undivided reality which takes concrete form in each respective historical context.”
Then the document discusses the relationship between the Old and New Testaments and Covenants. It begins by noting that God's covenant with Israel is irrevocable and that “the permanent elective fidelity of God expressed in earlier covenants is never repudiated. The New Covenant does not revoke the earlier covenants, but it brings them to fulfilment.”