Ah one thing, that might need to be changed/updated is the /var/www/nc/.htaccess, please run:
sudo -u www-data php /var/www/nc/occ maintenance:update:htaccess
Is there some reason why you symlink from /var/www/* to /var/www/nc? Why not just placing the files directly into the latter? I see benefits of symlinking only, if you actually want to preserve the old path, but need a different physical location, but as you want to achieve the opposite… 
?
Good point, I did not notice the .htaccess file.
Not sure I understand your question about the symlinks.
What I have on filesystem in /var/www/ looks kind of like this:
nc13.0.0 # This is where the NC installation is for 13.0.0
nc13.0.2 # Similar for 13.0.2
nc13 -> nc13.0.2 # a symlink
nc -> nc13 # a symlink
oc -> nc13 # a symlink I want to get rid of
And in my Apache configs I currently have /var/www/oc and I want to use /var/www/nc instead. And then in the web browser I would use https://my.domain/nc instead of current https://my.domain/oc.