thanks for your reply and the help with this issue. It is working now with only port 4433 forwarded.
Here is the solution:
As I am forwarding a non-standard port (4433) for SSL/TLS connections to my nextCloud server (which itself is listening on port 443 in my private network), I have to make sure that DAVdroid uses port 4433 aswell.
Though DAVdroid was set up like this using the standard URI www.example.com:4433 it did not work because using the short version of the URI and not the one actually pointing to the WebDAV interface (for nextCloud: www.example.com/remote.php/dav) resulted in the well-known URIs kicking in. Unfortunately, I did not change them to forward to port 4433 but kept the standard version of my nginx config.
So, the well-known URIs where forwarding to the standard port for SSLL/TLS. And that’s why it worked when I opened port 443 in addition to port 4433.
Hope this will be of help for someone who also uses a non-standard port 🙂
Thanks again and best regards.