I have Android Marshmallow on my Cyrus CS24 and Davdroid installed.
When I try to create a new contact the davdroid account is missing. (See picture)
When I create a new contact on my pc and sync it with nextcloud it is appearing on my phone but not "syncable". When trying to edit it appears: "Only phone, not sync......."
BTW: In acalendar+ my DAVdroid calendars are working!!!
DAVdroid missing when creating new contact in mobile phone
I think your manufacturer has made a faulty contacts app if it does not show. You can try in your contacts app if it is an option in "Contacts to display". Otherwise you need to try another contacts app. Maybe "True Contacts" - this is an unbranded Android contacts app!
One must still have chaos in oneself to be able to give birth to a dancing star. – Friedrich Nietzsche