I'm definitely not an expert, either, but I think they probably say that they want a paper from a "masters" because they want to avoid unpolished undergraduate papers. I actually found it really helpful to follow an online guide I found to drafting a new essay almost from scratch. (It was an old paper, but I revised it a lot.)
The guide is here: https://www.amazon.com/Arthur-William-Wright/e/B08CL4ZTN1/ref=dp_byline_cont_pop_book_1
Basically, it walks you through the steps to drafting a graduate school writing sample in the humanities: laying out your literature review, methodology, and theoretical framework; analyzing your archive of sources; and explaining the consequences for future researchers.
I do think, though, that drafting a new essay or really heavily revising an essay is the way to go. At least for me, the work I actually did for courses was too specific to those courses. It did not fit my application portfolios.