How to connect php-fpm with nginx?

I have a server that uses Nginx and PHP-FPM (PHP v7.4). It was working as well, I executed the following command for some reasons:

apt-get --purge remove php-common

After that, I executed this:

apt-get install php-common php-mysql php-cli

Commands executed successfully, but I get 502 error when I want to access websites on the servers:

It should be noted, there are several projects on this server. And I have nothing inside /etc/nginx/sites-available. I have all configurations under /etc/nginx/conf.d. See:

Each of them is a project. Now, I guess I need to set to PHP-FPM to use conf.d instead of sites-available. Any idea how can I do that?

Could you please help me how can I debug it?

You must make sure you have reinstalled the required software specifically the php-fpm

sudo apt-get install php-fpm

Then start the php fpm as follows

sudo systemctl start php7.4-fpm
sudo systemctl enable php7.4-fpm

Also make sure the php-fpm is properly setup in the server.conf of nginx. Which as per you must be OK as you havent changed it and it was working before your purge commands

server {
    listen 80;
    server_name example.com;
    root /var/www/example.com;

    location / {
        index index.php index.html;
    }

    location ~ \.php$ {
        include fastcgi_params;
        fastcgi_pass unix:/run/php/php7.4-fpm.sock;
        fastcgi_index index.php;
        fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
    }
}