I know about the normal sync… Your Cal part works fine… Syncing every 10mins… (nothing changed but still syncing)
This is quite unusual and should not be.
The server in the case has been changed for the contacts, but its been over 24 hours since I created the contact on the server and its still not synced to the local device.
Since it’s not documented by Android how long the period for automatically is (»Use this option if you don’t have to force a data transfer in response to data changes, but you do want to ensure your data is regularly updated. Similarly, you can use this option if you don’t want a fixed schedule for your sync adapter, but you do want it to run frequently.«), it may be longer then 24 hours on your device. If you explicitely need an update, I suggest to sync manually.
I don’t think it makes sense to sync every N minutes because this would waste resources, including power and battery.
But I still have to say that both the 10 minutes interval and the >24 hours interval are quite unusual.
I know its not fair to compare but when you update a contact in Gmail contacts, it pushes it to the phone within 1min.
As you say, it uses pushing which is not available via CardDAV.