I'm pretty certain you can still transfer to devices using the OD App from the Microsoft Store, they just moved things around with the new UI as you mentioned. This seems to be the FAQ about it?
https://help.overdrive.com/customer/...ticles/2295702
EDIT:
Looks like they did move the default storage location for the app. On my machine, audiobooks are now stored here:
C:\Users\[USERNAME]\Music\My Media\OverDrive