Yeah, those settings are for individual urls, not site-wide.
In forge, go to the "old.site.com" "site details" settings page. Scroll down to the bottom of the page. There is a "files" dropdown button. Select "Edit Nginx Config" from it. You'll get a popup containing the current config.
This should be your site definition to redirect everything from old.site.com to new.site.com.
server {
listen 80;
listen [::]:80;
server_name old.site.com;
return 301 http://new.site.com$request_uri;
}
That will redirect all urls to old.site.name to new.site.name, including any parameters. So, http://old.site.com/something/else would redirect to http://new.site.com/something/else
Instead of deleting everything that currently exists in the config for that site, I would comment out each line with a # at the beginning of the line, just in case there is a problem. Or better, if you know how, backup that config file before editing (via ssh).