The details are very vague. I need more details to suggest a solution. Like config files, logs of each service. potentially the link to your frontend as well as your nginx config file.

These are the backend logs, only this appears, attached there are my nginx, the frontend logs:
[27/May/2025:03:56:52 +0000] "POST /example_api_call HTTP/1.1" 504 569
[error] 4#4: *1 upstream timed out (110: Operation timed out) while connecting to upstream
Nginx.conf.template:

server {
  listen 80;
  server_name localhost;

  root /usr/share/nginx/html;
  index index.html index.htm;

  location / {
    try_files $uri $uri/ /index.html;
  }

  location /api {
    proxy_pass http://${BACKEND_URL_WITH_PORT};
    proxy_set_header Host $host;
    proxy_set_header X-Real-IP $remote_addr;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header X-Forwarded-Proto $scheme;
  }
}

In your nginx config file is this your actual url "${BACKEND_URL_WITH_PORT}" or is that just a placeholder you gave me?

If that is actually what you are using then can you change it to the actual private domain mentioned in Settings -> Private Networking ?
This should be your backend.railway.internal:8080
replace "backend" with your service name and "8080" with your backend's actual port

If that doesn't work then replace the api block with this

location /api {
    # Use Docker's internal DNS resolver.
    # The 'valid' parameter specifies how long Nginx should cache the resolved IP.
    resolver 127.0.0.11 valid=30s;

    # Set the backend address as a variable.
    # Using a variable triggers Nginx to use the resolver.
    set $backend_upstream backend:3000; # 'backend' is service name, 3000 is internal port

    proxy_pass http://$backend_upstream;
    proxy_set_header Host $host;
    proxy_set_header X-Real-IP $remote_addr;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header X-Forwarded-Proto $scheme;
  }

This is a variable that is currently being replaced in the build of the frontend, i confirmed it in the build logs, but i am using port 5000, since in my backend dockerfile i do

CMD ["gunicorn", "-b", "0.0.0.0:5000", "app:app"]

The problem isn't your frontend. It's nginx not being able to connect to your backend because the url you provided to nginx is incorrect.
The connection to backend is getting timed out so your frontend also doesn't get anything.

This is your network flow right ? Frontend -> Nginx -> Backend ?
If nginx isn't working then frontend won't either.

Replace the config api block with what i have provided. replace "backend" with your backend's service name and "port" to your backend's actual port which should be 5000 according to your dockerfile

I used the block below(with my actual backend service name) and now all my requests to the endpoint return 502 status after 30 seconds:

  location /api {
    # Use Docker's internal DNS resolver.
    # The 'valid' parameter specifies how long Nginx should cache the resolved IP.
    resolver 127.0.0.11 valid=30s;

    # Set the backend address as a variable.
    # Using a variable triggers Nginx to use the resolver.
    set $backend_upstream (my_backend_name_here).railway.internal:5000; # 'backend' is service name, 3000 is internal port

    proxy_pass http://$backend_upstream;
    proxy_set_header Host $host;
    proxy_set_header X-Real-IP $remote_addr;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header X-Forwarded-Proto $scheme;
  }
}