The NT is not the first instance in which the Greek word for church (ekklesia) is used. It was used in the Septuagint, the Greek translation of the OT–which was the translation used by the NT Church in spreading the Gospel. Often, but not always, it referred to the congregation of Israelites.
What Jesus DID inaugurate, through the shedding of His blood, was the New Covenant --a covenant which according to Jeremiah 31:31ff was very specifically made with “the house of Israel” and 'the house of Judah"–i.e., the Israelite (Jewish) people. Thus, it is understandable why NT Jewish Christians struggled to understand how non-Jewish believers in Jesus could be saved outside of becoming converts to Judaism. Cornelius and his household’s receiving of the Holy Spirit (which, if you study the covenants of the Bible, is the seal of the New Covenant) laid the foundation for the Council of Jerusalem’s decision about “the Gentile question” of Acts 15. In Ephesians 2, St. Paul explains how the Gentiles were “aliens from the commonwealth of Israel,” “strangers from the covenants of promise, having no hope, and without God in the world”–but through the blood of Christ became “fellow citizens with the [Jewish] saints and of the household of God.” Jesus death not only brought a new covenant for the Jewish people who received Him, but it opened the door for believing Gentiles to become part of the covenant people of Israel.
“Binding and loosing” was a Jewish term that referred to the authority which spiritual leaders (typically, the Sanhedrin) had in making legal decisions and similar types of rulings. Among the Jews, it never included the power to forgive sins, as it does in the RCC.
My point: Since the Bible is, for the most part, a book penned by Jews who wrote from a Hebraic cultural and theological frame of reference, I think it is important to consider these things in interpreting the meaning of the scriptures, particularly in reference to NT theology. Gentile Christians, both Catholic and non-Catholic, haven’t always taken the Hebraic context into consideration.