After changing on a server and syncing one more time I still don’t see neither new contact neither new group on the phone.
I don’t remember DAVdroid version I’ve used at time of initial setup but given that it was in September it probably was 1.3
Since then I’ve also upgraded Android (as I remember Adroid version 6.0.1 hasn’t changed at this update).
It seems to be that new contact was stored on the phone. I’ve added email to this new contacts and it now appears in mail client autocomplete.
It will be great if your will add more verbose log about group creation. Can you suggest some 3rd party contacts app to see if new contact is shown there? Stock contacts app probably doesn’t show it because group was not added.