Configure two different nginx port to setup two different magento version website

I want two setup two different version of magento 2 on my local nginx machine, v2.4.2 and v2.3.7 mapped with two different domains.
One version(2.4.2) is working fine on my nginx server at port 80 with domain- http://magento.local.in/ folder location /var/www/html/magento. Below is the nginx config file- /etc/nginx/site-enabled/magento (same config in site-available)

upstream fastcgi_backend {
  server  unix:/run/php/php7.4-fpm.sock;
}

server {
  listen 80;
  listen [::]:80;
  server_name magento.local.in;
  set $MAGE_ROOT /var/www/html/magento;
 
  include /var/www/html/magento/nginx.conf.sample;
}

Now I want to setup another version(v2.3.7) at same server with different port (lets say 81). So I downloaded version files and successfully installed at location /var/www/html/magento23

I thought(not sure) new nginx config file would work perfectly for this so I created-

/etc/nginx/site-enabled/magento23

server {
  listen 81;
  listen [::]:81;
  server_name magento23.local.com;
  set $MAGE_ROOT /var/www/html/magento23;

  include /var/www/html/magento23/nginx.conf.sample;
}

I am able to run every bin/magento command in the same directory magento23 but site is not accessible in the browser-

This is the /etc/hosts file –

127.0.0.1       magento.local.in
127.0.0.1:81    magetno23.local.com
127.0.1.1       prm

# The following lines are desirable for IPv6 capable hosts
::1     ip6-localhost ip6-loopback
fe00::0 ip6-localnet
ff00::0 ip6-mcastprefix
ff02::1 ip6-allnodes
ff02::2 ip6-allrouters

I do not understand why these two completely different project are not working. I think it could be done by single nginx config file but do not know how. I have tried to much to dig this and also follow some solutions as well –
https://askubuntu.com/questions/759513/how-to-run-multiple-magento2-setup-with-nginx

Magento 2: How to configure Nginx to use multiple websites with sub-folder

But nothing worked because I am not doing one setup with multiple website, store or store view. I am trying to setup two different independent versions with no dependencies.

Can anyone want to help me out here with the correct approach. Thank you.