Peter was the Apostle to the Uncircumcision as Scripture clearly says. He visited areas of Asia Minor where the "sojurners" [Jews} from Jerusalem werre scattered -- not Rome. Rome is never mentioned. And when he wrote his First Epistle from Babylon, where there was a large Jewish community and scholars busy compiling the Babylonian Talmud, he addresses it to those "sojourners from Pontus, Galatia, Cappadocia, Asia, and Bithynia". He never wrote from Rome nor wrote to Rome.
Very few Jews were Roman citizens and unless one was a Roman citizen, they were personna non-grata in Rome, visitors only. Paul was a Roman citizen but Peter was not.
It is true that Rome does not officially recognize Anglican orders, but this has nothing to do with the papacy. And they do not question the validity of the Eucharist in Orthodox churches. The doctrine of the Eucharist has nothing to do with Peter and the papacy. The doctrine has clear scriptural support and has been the principle worship service of all catholic (little "c" intended) and apostolic churches since the very earliest days.
Very few Jews were Roman citizens and unless one was a Roman citizen, they were personna non-grata in Rome, visitors only.
I can't comment on the accuracy of this statement, but I believe Josephus and other historians mention fairly large and well established populations of Jews in Rome.
You should write a book about all this stuff you don't know.
The Orthodox maintain a valid priesthood and their sacraments are considered valid. Amglicans have some valid priests, but as a rule, they've made a big mess of it. Once they started "ordaining" women any serious effort to maintain a valid priesthood was lost.
It has to do with Apostolic succession more than with Peter or the keys. And very little to do with Rome. If Peter never set foot in Rome, there would still be priests descended from the Apostles. If Jesus came a few humdred years later, then Constantinople would be the seat of the only Church.
SD