Here is a working example where an Apache reverse proxy is running on the host.
https://help.nextcloud.com/t/howto-ubuntu-docker-nextcloud-talk-collabora/76430
I don’t use nginx, so I’m not sure I can offer much there, however one thing that stuck out to me was you mentioned you couldn’t connect to CODE from NC. What I do in my setup is have them both connect to each other through the reverse proxy on the host, where they are both presented valid certs by the proxy. And I used the docker-compose extra_hosts directive to make sure they both resolve the names to the LAN IP of the host.