What is the origin of the Orthodox belief that Sts. Joseph and Mary were betrothed but not married?

The Orthodox refer to St Joseph as [Joseph the Betrothed](https://orthodoxwiki.org/Joseph_the_Betrothed) . They assert that he and the Virgin Mary were betrothed, but never married. This differs from the Catholic and Protestant belief that they were married. What is the origin and history of this belief? In teachings about Joseph where the Orthodox and Catholic differ, the Orthodox seem to align with the Protoevangelium of James. However, I don't see a perpetual betrothal mentioned there. There are places where Joseph denies marrying Mary 'in stealth', but this occurs during her pregnancy with Jesus. I don't think those can necessarily be used to show that they weren't married later. Related/Inspired by [How old was St. Joseph when he married the Blessed Virgin Mary?](https://christianity.stackexchange.com/questions/59756/how-old-was-st-joseph-when-he-married-the-blessed-virgin-mary) .