Handling Nginx location aliases when using a standalone PHP-FPM server

I host various Laravel applications that use various versions of PHP, and decided to improve the current single bloated container Docker setup by having multiple PHP-FPM containers, one for each PHP version.

I tested the setup by having a PHP file at /var/www/html/index.php mounted to all containers and it works as expected.

However, since Laravel apps are served from a public subdirectory, this causes issue when the PHP container tries to find the file.

This is the Nginx config:

location /appname/ {
        alias /var/www/html/appname/public;
        index index.php;

        # Use PHP 7
                location ~ \.php$ {
                        fastcgi_pass php74:9007;
                        fastcgi_index index.php;
                        include fastcgi_params;
                        fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
                }
    }

So a request to /appname/index.php actually gets served from /var/www/html/appname/public, but the PHP containers don't know this and can't find the file.

I tried replacing $document_root with /var/www/html/appname/public or /appname/public but neither worked.

This is the error PHP-FPM is throwing:

FastCGI sent in stderr: "Primary script unknown" while reading response header from upstream

How do I go about letting PHP know the path to properly serve the app?

Feel free to recommend a better container setup to achieve this goal.