Specifically, the choice to use it without the characters having any reason to be made of paper, without making paper jokes/puns (or really any themed puns in the game whatsoever, aside from Unbeelievable), while also telling a story that is far from lighthearted and comical?

Personally, I think that it should have gone with its own aesthetic. Due to the reasons above, I find the art misleading for the experience. And it feels like it was specifically meant to be misleading in order to draw an audience - or at least, if not intentionally misleading, they simply tried and failed to give a Paper Mario experience (aside from the aesthetics and some aspects of combat).