You can search by genre in the Kobo overdrive interface. Just search for "fantasy" or whatever instead of the author or title in the search bar. My library also sets up a rotating set of collections of recommended books of different sorts, which is very nice for browsing.
The UI will also only show ebooks which the Kobo can fulfill for you (which is not exactly the same thing as Libby's "epubs" category, but is useful if you don't want to mess around with download & transfer). I don't know any way to explicitly filter by availability, unfortunately, but "most popular" seems to bias the top of the list towards available books.
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