There are three sections of the library, "I'M READING", "PURCHASED", and TRASH". When you first enter your library it only shows the "I'M READING" section. Have you checked the "PURCHASED" section? (If you don't use a Kobo device or app then it doesn't really make any difference which section they are in, but you can bookmark a book in the "PURCHASED" section to make it appear in the "I'M READING" section if you like.)
FWIW all of my books show in the "PURCHASED" section with a download button, regardless of which address I used to buy them, even if they are books that are not available in my current geographical location. But I have noticed that sometimes the book I see from my library is not exactly the same book as seen when browsing the website. I think this is usually because the publisher has updated the book, but the one in my library is still the old version. (Kobo won't update the book in your library unless you complain that there is something wrong with the old one).
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