I stopped and chatted for a few minutes with Steve Potash and some other OverDrive folks that I knew by email. Steve confirmed that OverDrive have been rolling out the Kindle library ebooks over the past few days and that all of OverDrive's partner libraries should now have the new service enabled.
I also learned, quite accidentally, that my library finally has ebooks. The Prince William County Library is up to about 500 ebooks now in addition to the audiobook collection that I already knew about. So far as I can tell, neither OD nor my library announced the new content.
If you're curious about whether your library has ebooks then you might want to visit OverDrive website and search their list of partners. You might also be interested in a pair of instructional videos on checking out ebooks and returning them early.