Did modern Church apologized to Galileo Galilei?
Yes, it did. The decisions in the Galileo case were disciplinary or procedural, not doctrinal matters at all, even though some individuals in the Church at the time thought they were. The infallibility of the Church attaches to its officially proclaimed dogmas, such as Christ’s two natures or Mary’s Immaculate Conception. These are matters of the highest authority. The Church cannot be wrong in these matters. But in matters of empirical science or anything that is not what is called de fide, the Church can and has made many reversals. If these had been matters of dogma, the Church could not have reversed itself. The the pursuit of knowledge is always a humbling process. And that is good, because humility is one of the greatest virtues. Peace and every blessing!