When you say library, do you mean they are linked to your account? Or just in a collection?
https://itch.io/my-purchases vs https://itch.io/c/27734/letsmaybelp92s-collection are two different concepts. The first link is games you properly own (and you can't really share that publicly. The second link is a collection I curated, which include both free games, games I own, and paid games I don't own.