As you've well-noted, there is nothing in Scripture about any apostolic succession. There is only apostolic teaching, passed down through Scripture.
The snippets of quotes Rome pushes forward as some kind of evidence shows just how desperate Rome is to substantiate its error. They take a line here and there from some translation of something and cobble it together to say the pope and his magisterium are infallible in matters of faith and religion when Scripture teaches only Christ is infallible and His teachings are what men are to follow. Teachings found in the Bible, open to all.
Not true of "Rome" but definitely true of Calvin, qv above in your quoted passage.