Three months late, but there's a mechanical explanation for why Itch.io doesn't show Ironsworn in your library by default: it doesn't show any free PDF that wasn't, "claimed," like a community copy of an otherwise premium title, as, "owned," in your library. Anything that isn't classified as a purchase doesn't register.
This also has knock-on effect of making games *really* hard to track down again if you lose them or don't manually write down every single thing you download just to remember. In the event you lose the game and it's been taken off Itch.io for some reason, you also can't back it up from your library... because Itch.io neglects to store anything you got for free.