auto-detection of resources with current-user-principal, getting & querying home sets (just like DAVdroid), and then
detect if the entered URL is a directly usable resource (without using auto-detection).
I guess this is because CardDav-Sync wants to support resources without auto-detection, whereas DAVdroid only supports auto-detectable resources.
The /shunyata/addressbook-Default/ resource isn’t made available for auto-detection by eGroupware (and that’s not the fault of DAVdroid, because CardDav-Sync doesn’t receive the /shunyata/addressbook-Default/ resource in the auto-detection process, too – just look for addressbook-Default in the logs), this resource is not supported.
This is not a DAVdroid issue but an eGroupWare issue. If you need group addressbooks, I suggest to create an enhancement/bug request in the eGroupware tracker.
java.net.ProtocolException: unexpected end of stream
This means that the server interrupts the connection while the transfer. I guess it’s a problem either of Radicale of your intermediate Web server (if you have used one). Did you have a look at the Radicale / Web server logs (maybe you have to increase verbosity)?