Libby/Overdrive? It’s great, except for the 12 weeks I’m waiting for most of the books I want, then they become available during time that I don’t have to read.
I've started collecting libraries (cards) from each place I live. Libraries will often have more than one digital service (Overdrive, Hoopla, Borrowbox), and each library may have sharing agreements with neighboring systems.
I use the Chrome Instant Multi Search extension to search all the libraries+services – about 12 different sites at this point. Between them they have almost every book I want in e-book or audiobook, and by placing holds I can keep a steady queue of books going. Managed 125 books this year that way, the majority of them digital, and free.
Yes, it is like a physical book where the library has a given number of books to lend at any time, and you get to borrow it for a specified time window. Likewise for audiobooks and videos. You have to use the Overdrive app (US users can also use Kindle for e-books). It is insane and exactly what I've come to expect here in the US.
The trick (at least on a kindle) is that a book loan doesn’t get marked as closed until you go to the homescreen. Just have to be very careful to avoid that button!