Hide port number in URL exposed by NGINX Docker container

I run Docker NGINX container with exposed ports 8080 and 8443.

So I visit welcome NGINX page at: http://www.nginx.test:8080

I'm trying to figure out IF it's possible to hide/remove port in URL.

So I visit welcome NGINX page at: http://www.nginx.test

Since the NGINX is reverse proxy server it should work. Still new to NGINX and I had to Google some answers and basically they are applied in tries bellow.

First I tried (didn't work) NGINX's directive proxy_redirect at server level like this:

server {
    listen 8080;
    listen [::]:8080;
    server_name www.nginx.test;

    proxy_redirect $scheme://$server_name:8080 $scheme://$server_name;
}

Then I tried (didn't work) NGINX's directive proxy_pass at location level like this:

server {
    listen 8080;
    listen [::]:8080;
    server_name www.nginx.test;

    location / {
        proxy_set_header Host $host;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_pass $scheme://$server_name;
    }
}

Probably there's more than that to make it work.