“I want to move a row to a different page, but the two pages have different columns.”
When moving or copying rows from one page to another, the columns get mapped from left to right, regardless of column type or width. So, a text cell may end up in a date column and vice versa.
This is okay, and the values aren’t changed. You can see them by adjusting column widths; you can move the values to different columns of appropriate type.