Kobo only integrates with OverDrive, the predecessor to Libby. You can only use one library card at a time with OverDrive, and don't have access to the audioboks or periodicals on Libby. Meanwhile Kobo will aggressively push you to sign up for their monthly subscription to get access to that kind of content.
If you want Libby on e-paper, sans Kindle, your best bet is to look at the E Paper android tablets (I use Boox) and just install the Libby app. The experience isn't perfect but its the least worst option.