I have a flute part that’s clearly in the setup list but does not exist in my layouts section, print section, or when I look to create a new tab for the part only.
See screenshot of Print.
Welcome to the forum! Although your flutes exist as Players in the panel on the left, if you look at the panel on the right in Setup mode, there’s no Flute layout - that’s what’s important when determining which layouts exist in the project. Either create a new part layout by clicking the relevant button at the bottom of the Layouts panel, or choose Setup>Create Default Part Layouts - this restores all the parts that should be in your project, based on the players.
For some more information about how players, layouts and flows interact, see here.