Anglican really just means a version of the Catholic church splintered off by Anglo-Saxons
The proto-Anglicans stopped being Catholics when King Henry the 8th couldn’t get the pope to annul his marriage, so he split the English church from the Catholic church. So, for 500 years, the Anglicans haven’t been Catholics. And it has nothing to do with “Anglo-Saxons”. Anglo-Saxons are a cultural group from the middle ages. The Church of England and Anglicanism comes from centuries later and applies to the country of England under the king Henry the 8th. The Church of England and/or Anglicanism doesn’t date from the middle ages, it was effectively a political construction due to the king wanting a divorce and not to have to answer to the pope. But, the reasons behind the split don’t really matter as much as the fact that the people following churches related to that split haven’t recognized the authority of the pope for centuries, so they’re not Catholics.
In this case, the name is really misleading because the Anglicans don’t consider them to be Anglican, the Catholics definitely don’t consider them to be Catholics, and you can’t really merge the Anglican and Catholic faiths because they’re so different.
Like all Church schisms it’s “we’re the only ones who are right about how our god is supposed to be worshiped”, so they don’t feel bad about taking the names of Anglicans or Catholics because they think that those other groups are doing religion wrong, so who cares if it’s confusing.