Thanks to Lillelara, I've found the new library app (Libby) that seems to be a vast improvement over the Overdrive app. I spent last night playing with it, as a distraction from watching the Rangers lose yet again.
It works like Overdrive, in that it syncs with your library Overdrive account and allows you to download the books you've checked out. There are some enhancements on the audiobook functions, and a vast improvement on the ebook functions.
I've never been successful with the ebooks on Overdrive, as they seem to get lost when I try to download them, so I can neither read them nor return them until my checkout expires. I've only been able to do ebooks from Overdrive by sending them to my Kindle app. But I tried checking out, downloading, reading, and returning several ebooks on Libby last night, and they all worked just fine.
It's also more seamlessly integrated with the Overdrive library, which makes browsing for books much, much easier. It automatically syncs your checkouts and holds with the Overdrive library website, too.
My "wishlist" of almost 200 ebooks and audiobooks that I've carefully compiled and synced with my larger TBR list, using the Overdrive website, does not sync with Libby. It instead uses a "tag" system, which is completely separate, and is less than useful as you cannot see the book's availability when browsing your tags list. So, for example, if I want to check something out right now and start reading it right away, I can go to my wishlist on the OD website, and filter by "available", and browse through books that are already on my TBR list and are immediately available for checkout. This isn't possible on the Libby app. But, I can still do it from the OD website, check it out there, then open the Libby app to immediately download and listen/read.
It's still not perfect, but it's a huge improvement over the current Overdrive app. I might even start reading some ebooks, which is a good thing since so many of the books on my TBR are only available from my library in that format.