Graylog behind nginx sub directory how-to configure

I’m still not clear how this is a problem with Graylog. The thread in the LibreNMS Community you’ve linked to clearly shows that the Graylog REST API is accessible via http://<graylog-host>:8888/graylog/api.

Maybe the LibreNMS Graylog integration simply doesn’t work?

One wild assed guess: LibreNMS is using HTTP/1.0, while curl is using HTTP/1.1.
HTTP/1.0 doesn’t know anything about the HTTP Host header, so if your nginx is hosting anything other than Graylog (“virtual hosts”) and LibreNMS doesn’t perform a proper HTTP/1.1 request, it might not be able to serve the data it should.