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!
@daniu We did it intentionally without the “sync” flag in DAVdroid UI, because
for each calendar, there would have to be two “sync” flags: one for the events, one for the tasks,
it makes the whole thing much more complicated and error-prone.
The “simple” use case is just to check (or uncheck) the calendar in DAVdroid, and it will be added and synchronized (or not). If you’re going “advanced”, you may change the SYNC_EVENTS in your calendar app, but DAVdroid will only honor it and provide no GUI for that (for above reasons).