NGINX reverse Proxy- url configuration

I have three URLs for which I want to do a reverse proxy. (Also, the URLs can have an optional '/' at the end.)

1. /test
2. /test/id
3. test/id/{id_number}

So far I am writing the nginx config for the first one, but it seems I cannot get it right. This is my first time writing the nginx configurations. Can someone help me ?

I am currently getting this error currently -

2025/04/07 11:33:08 [error] 17#17: *18 rewrite or internal redirection cycle while processing "/test", client: 172.17.51.128, server: , request: "GET /test HTTP/1.1", host: "https://www.google.com/"

Here is my config file

http {


    upstream test_host {
        keepalive 25;
        server ${API_HOST};
    }

    server {
        listen 80;
        root /usr/share/nginx/html;
        index index.html;
        add_header 'Access-Control-Allow-Origin' '*' always;

       

      location ~ ^/test$ {
            gzip_types *;
            rewrite ^ $request_uri;
            proxy_set_header Host ${API_HOST};
            proxy_pass http://test_host/$1;
        }
    }
} ```