A reader has tipped me to a Chrome extension which lets users browse Amazon.com and see if a book or ebook is available at their local library. It's called Library Extension, and you can find it in the Chrome Web Store.
Once installed (and configured), simply browse book or ebook listings on Amazon.com, and Library Extension will insert an extra window above the buy button with info on whether your library has the title in its catalog. For some libraries, you can also browse the audiobook, movie, and music catalogs.
LibEx works with a lot of libraries in the US, Canada, and Australia, but not all. It can check a library's ebook catalog with OverDrive, Hoopla, or BiblioCommons, and in many cases it can also check a library's print catalog (which is a lot harder than it sounds).
If it finds a match it will offer the option of checking out the ebook or placing a hold As you can see in the screenshot below, my library doesn't have Lash-Up as an ebook and all the print copies are checked out.
Library Extension has been around since at least January 2013, but it started getting press again in 2019. I think it's a great way to reuse one of the better designed bookstore sites, but I do wish it weren't so limited.
It doesn't work with 3M Cloud Library, or most of the smaller library ebook vendors. While services like Freading are not as widely used as OverDrive, they still offer a chance for a reader to save money by not shopping at Amazon.