NGINX display first site in subdirectory of second

The problem is:

First site firstsite.test runs on PHP 7.4, I need to launch second site on PHP 8.0 and another framework inside its subdirectory: firstsite.test/second-site/

So, now I have 2 separate nginx conf for each sites and they are workinbg separately.

But I cant make second site to be shown on first site subdirectory. What I tried:

1. Make an alias in first site conf:

server {
 listen IP:port;
 root /var/www/user/data/www/firstsite/current;

 location @php {
        fastcgi_index index.php;
        fastcgi_param PHP_ADMIN_VALUE "sendmail_path = /usr/sbin/sendmail -t -i -f [email protected]";
        fastcgi_pass unix:/var/www/php-fpm/1.sock;
        fastcgi_split_path_info ^((?U).+\.ph(?:p\d*|tml))(/?.+)$;
        try_files $uri =404;
        include fastcgi_params;
    }

 location  ~ ^/second-site/ {
        alias /var/www/user/data/www/secondsite/current/public;
 
        add_header X-Frame-Options "SAMEORIGIN";
        add_header X-Content-Type-Options "nosniff";
     
        index index.php;
     
        charset utf-8;
    
        try_files $uri $uri/ /index.php?$query_string;
        
     
        location ~ \.php$ {
            fastcgi_pass unix:/var/www/php-fpm/18.sock;
            fastcgi_param SCRIPT_FILENAME $realpath_root$fastcgi_script_name;
            include fastcgi_params;
        }
     
        location ~ /\.(?!well-known).* {
            deny all;
        }
    }
}

2. Set root path:

server {
 listen IP:port;
 root /var/www/user/data/www/firstsite/current;

 location @php {
        fastcgi_index index.php;
        fastcgi_param PHP_ADMIN_VALUE "sendmail_path = /usr/sbin/sendmail -t -i -f [email protected]";
        fastcgi_pass unix:/var/www/php-fpm/1.sock;
        fastcgi_split_path_info ^((?U).+\.ph(?:p\d*|tml))(/?.+)$;
        try_files $uri =404;
        include fastcgi_params;
    }

 location  ~ ^/second-site/ {
        root /var/www/user/data/www/secondsite/current/public;
 
        add_header X-Frame-Options "SAMEORIGIN";
        add_header X-Content-Type-Options "nosniff";
     
        index index.php;
     
        charset utf-8;
    
        try_files $uri $uri/ /index.php?$query_string;
        
     
        location ~ \.php$ {
            fastcgi_pass unix:/var/www/php-fpm/18.sock;
            fastcgi_param SCRIPT_FILENAME $realpath_root$fastcgi_script_name;
            include fastcgi_params;
        }
     
        location ~ /\.(?!well-known).* {
            deny all;
        }
    }
}

Nothing of this works. Please, point me to right way.