The eschatological hope of the Samaritans was built around the Prophet like Moses and the figure identified as the restorer. It is lazy to divide the world into Jews and Gentiles, for the Samaritans were Semites, not Gentiles, and they did not see themselves as Jews either. John Chapter 4 makes a great deal of the Samaritans and the unexpected discourse on deep theology with a woman who did not come to this well with the other women, possibly in some sense an outcast or marginalised person, is profound. The role of the Samaritans in John is very significant, and if you compare the number of references to David, against the number of references to Moses (also The Prophet) is very telling. I wonder if one of the mistakes of our time is to over-emphasize the role of the Davidic line and minimise the role of Moses.
My point is that the eschatological hope of the Samaritans was very different to the eschatological hope of Israel. For the Samaritans, Jesus is the Restorer, just as he is the Messiah for the Jews. The end of this chapter accords the Christological title, Savior of the world - the Greek being soterion ton kosmon. I think translating is as Saviour of the Cosmos would be valid and appropriate. John 4 sets Jesus mission on a much broader canvas.
I like that interpretation.
I was thinking something similar to what you were saying, but more like, this was a time when talk of a Messiah-like figure became commonplace, and that Jesus' popularity, beginning with John and his baptismal ministry, intensified the anticipation enough that it eventually reached Samaria. The Samaritans, having been subjugated under the same oppressive rule as the Jewry, sought a new found eschatological hope in rumors about Jesus. This event with the woman at the well may have been the first encounter of any Samaritan with Jesus himself, and so he likely was largely unnoticed when he passed through their cities, unlike other places where Jesus travelled, he was immediately recognised. We do not find the woman quoting from their tradition, but states it like a generally accepted fact:
"The woman said to him, 'I know that Messiah is coming. When he comes, he will tell us all things.'" (John 4:25).
This statement leads me to believe that she said this on Jesus' account. She wanted to take advantage of this unique opportunity, after discussing a broad range of personally sensitive subjects, with a religious Jew. He confirms his identity to her:
"I who speak to you am he." (John 4:26).
What happens next?
"So the woman left her water jar and went away into town and said to the people, 'Come, see a man who told me all that I ever did. Can this be the Christ?' They went out of the town and were coming to him." (John 4:28-30).
Did they examine his words like the Pharisees and lawyers? Did they test him like the Sadducees and Herodians? Nope. We do not find a Berean among them. Instead, we read:
"Many Samaritans from that town believed in him
because of the woman's testimony." (John 4:39)
It seems that they were like the Athenians, who, "spend their time in nothing except telling or hearing something new" (Acts 17:21).
I believe that their eschatology was on the fly of the times. They sought relief and freedom and clung to the Jewish hope among many others.