If for some reason adding a PHP-FPM pool doesn’t work, and you don’t know why, and you’ve spent 20 minutes bashing your head on it even though you’ve added the config file and everything.. make sure you’ve remembered to change the poolname at the top of the file from the [www] you copied from the www.conf file
I know most folk these days are using ansible and stuff to do this, but we add sites so rarely it’s just not worth setting up