Lost or found: the northern tribes

Last week our family read the following story from Luke 2:36-38:

And there was a prophetess, Anna, the daughter of Phanuel, of the tribe of Asher; she was of a great age, having lived with her husband seven years from her virginity, and as a widow till she was eighty-four. She did not depart from the temple, worshiping with fasting and prayer night and day. And coming up at that very hour she gave thanks to God, and spoke of him to all who were looking for the redemption of Jerusalem.

I'm quite sure I've read this story many times over the decades, but this time I happened to notice that her genealogical origins were in the tribe of Asher, one of the ten northern tribes carried away by the conquering Assyrians more than seven centuries earlier. Most of the references in the New Testament are to Judah (Jesus himself) or Benjamin (Paul the Apostle), which were part of the historic southern kingdom of Judah.

This account of Anna's origins makes me wonder whether the northern tribes were also subject to the Persian king Cyrus' edict allowing the Jews to return to their land. It also makes me wonder about the origins of the Samaritans of Jesus' day, since the northern tribes were apparently among their ancestors. If Anna was descended from one of these northern tribes, then why was she worshipping at Jerusalem rather than at the site of the Mt. Gerazim temple destroyed by John Hyrcanus during the Hasmonean period? In short, why was she not considered a despised Samaritan?

If anyone knows the answers to these questions, I'd love to hear them.