I emailed my library's help desk to ask about this issue. Who knows if I will get a knowledgeable person with a useful answer, but I figured it was worth a try. If they report back that Overdrive is officially no longer going to support direct access for Sony readers, then at least I'll know for sure and I can decide whether I want to just keep the Sony and get my library books via PC (I do that most of the time anyway) or whether being able to occasionally get books directly on the reader is important enough for me to switch readers.
I noticed that Overdrive still has a help article on how to get books on a Sony reader
http://help.overdrive.com/customer/p...ticles/1481653
If you scroll down toward the bottom it includes instructions on getting a book directly on the reader. Note that below the article says "updated October 3, 2016" - pretty stupid for them to post this article if it's no longer possible to use a Sony reader in this way.