nginx.conf file to log requests/responses related to a specific domain ?

Hello, I have troubles using my Supabase postgresql database on

It seems it has something to do with the responses received from Supabase, which I would like to log.

My goal is to see those logs in the “monitoring” section of
I’m a newbie in all this, but I think I understood this might be achieved using a nginx.conf file.
Am I right on this ?

Here’s what I’ve got so far, but I don’t see any log in the monitoring.

user nginx;
worker_processes auto;

error_log /dev/stdout info;  # Log errors to stdout for Fly
pid /var/run/;

events {
  worker_connections 1024;

http {
  default_type application/octet-stream;

  log_format main '$remote_addr - $remote_user [$time_local] "$request" '
    '$status $body_bytes_sent "$http_referer" '
    '"$http_user_agent" "$http_x_forwarded_for"';

  access_log /dev/stdout main; # log requests to stdout
  sendfile on;
  keepalive_timeout 65;
  gzip on;

  server {
    listen 80;
    server_name _;
    keepalive_timeout 5;

    location / {

      # Log proxy responses
      access_log /dev/stdout main;
      error_log /dev/stdout info;

Thanks for your help!